I did my best to answer your question and answered as I understood what troubled you. Though , you didn't really formulate a question but expressed being somewhat upset, I believe I understand what you meant, but it is probably the best to allow me to clarify things some more.
I agree with you 100 hundred percent that both a kolel student and a religious soldier are "avdei Hashem", though one on the individual level and the other more on a national level.
And of course as parents and teachers we want to see our children grow up serving Hashem in the fullest way by learning torah and keeping Mitzvot. This is also clearly the view of the Mamlachti Dati system,
The question is how to view the non-religious soldier who is willing to be "moser nefesh" to sacrifice his life to protect the State of Israel and the Jewish people. And we can include in our question not just the soldiers but the original settlers who came to Israel more than a hundred years ago and also Jews who view themselves as "secular" but still make "aliya" to Israel today. Are we to view their actions as secular patriotism /Zionism without any association to something holier? Are they indeed just "secular"?
My understanding of what bothered you with your children's response to your question was their ability to see in the non-religious soldier as somebody who is actually serving Hashem. On that point, as we shall see in the lines to follow below, that this soldier actually his. He is not just a secular person doing his civic duties and expressing nationalistic or social values.
On this particular point my esteemed colleague, Rav Moshe Kaplan shlit"a , (who used to also answer questions on this website ) has been lecturing extensively for many years. I therefore asked him to draw up some notes to explain this view. He made efforts to make it concise ,but nonetheless it is a bit more lengthy than answers which usually appear in this site. Since the subject is of major importance, I decided to include what he wrote in my answer. I therefore request of you to have patience and read what he has to say carefully.
1) There is a halachic discussion regarding a mitzvah done without intention. Is doing a commandment a mitzvah even without doing so as a G-d given mitzvah, rather out of human, moral motivation? Is there any spiritual significance to the doing of G-d's will in and of itself - independent of intentions (although there is no question that the ideal is doing with full intention, but even in that there are many levels as well: doing out of fear of punishment; desire for reward(1); lishma; for the uplifting of all Creation; with the kabbalistic intentions, yehudim and kavanot...). There are those that say the commandment of Yishuv Eretz Yisrael is fulfilled even without intention, and they bring what our Sages say that Esav had the merit of dwelling in Eretz Yisrael.
2) On this specific point there is an amazing Pele Yoetz, sv. hatzala, which states that those who save the lives of other Jews "surpass the wise and gedolim of Israel" because of this mitzvah - even though "they seem to us as so empty of mitzvot (=secular)."
Also from the book Hessed L'Avraham (by the great Kabbalist, Rav Avraham Azulai, grandfather of the Chida) we see that we cannot judge by simple, external standards. He writes (ibid. 3:12): "All who dwell in Eretz Yisrael are considered a tzaddik (righteous) even though he does not seem to be according to what we see... even if he is known as an evildoer."
3) But beyond the above, to properly judge matters like this, a broader perspective is required and we cannot judge the phenomenon simply by its momentary manifestation. True evaluation can be made only when seen in context - the moment as part of a larger process. If we judge an isolated point on the timeline, based upon what it looks like at the moment, seeing what is presently revealed, we can misjudge - and misguide. "The wise sees the nolad" - what is growing and developing inside. Where coming from and where going. The perspective of Emunah sees beyond what the camera picks up - the frozen, isolated moment, external facade, rather sees what is pushing and unfolding (as the vision of Rabbi Akiva - see end of Makkot).
So on a deeper level we must ask: What truly drives that soldier to "serve the nation of Israel and put his life on the line"? Just human, secular considerations (as he himself says), or upon deeper analysis do we see that indeed it emanates from a "hidden," subconscious (superconscious - Neshama) drive to do G-d's will?
Those dedicated to defending the Jewish people in our land are part of the amazing process of redemption - our national revival and return to Eretz Yisrael. This return is indeed not complete, but as our Torah sources tell us, it will take place in stages(2). At the beginning they are doing great things, propelled by, and fulfilling, the word of G-d and His prophets, but "instinctively," from a natural inclination to do so - without the awareness that it is a mitzvah. Later comes the advanced stage of being consciously aware of the Divine source and content of those actions. That is how things develop in our world - not all complete all at once - just as children go through stages of development, and we must see each stage in the context of that developing personality.
So technically it may be that they are not considered fulfilling the commandment because Hashem commanded. But again, if we do not just measure by the moment, but see what we have before us and what Hashem is doing, we see amazing, Divinely "charged" souls. The willingness to sacrifice for the sake of others and an unselfish dedication to the collective are indications of a strong illumination of the collective soul in them (which is not a product of their understanding, but the "superconscious") that causes them to be so connected and devoted to the klal. Indeed the Sfat Emmet writes (Parshat Kedoshim) that the only way to merit holiness is by dedication and connection to Klal Yisrael. That is why we say before the mitzvot that "I do the mitzvah... in the name of all of Israel." These souls may not be saying that - but they LIVE it.
This soldier has an unselfish desire to defend the Nation of G-d and the Land of G-d - which is G-d's will - he is serving G-d without knowing it! That is certainly not complete, he is doing so "instinctively," and we must bring him to the awareness of the great signifiance of his actions, that he is serving the Divine and bringing a greater blessing to the world than what he thought. Nevertheless, in a deep sense, paradoxically, he is serving the Divine ideal, but is presently not consciously aware of that fact.
Just as the entire process of our national rebirth can be seen as driven by secular, human ideas, but the eyes of Emunah teach us to see the Divine spirit ("I will put My spirit in you and you shall live" - Yehezkiel 37:14) which is infusing, inspiring the nation to get up and return to its full grandeur,(3) even if the participants themselves are unaware of that source.
It is not up to them to take Hashem out of the picture. If they say Am Yisrael is not the holy nation of Hashem, then we cease to be the nation of Hashem?! That is the objective reality(4) - just as every Jew has a Neshama whether he claims all day he does not and that he does not even believe in Neshamot! It is not dependent on his awareness or agreement. Of course the ideal is to be aware of that Divine content and run our lives accordingly - but who will that come from if we ourselves fail to see the inner Divine hand, and agree that there IS NO Divine content since they say there is none?! We have to be aware and reveal to them the true holy essence of our being, who we really are and then can show how to live up to that content in our daily lives.
So to summarize the above point, these soldiers are doing a mitzvah but without the name of G-d on their lips or on their conscious minds. But the fact that the nation is waking up to do G-d's will, that stems from the inner Neshama(3a) that is coming to expression in stages, from the natural, instinctive stage to full conscious awareness.
So it could be your children have a natural tendency for the holistic perspective, seeing or sensing and appreciating the value of the stages in the context of the process, and the assumption of your question was seeking judgement based on the momentary, revealed level.
(1) By the way, we can ask about ourselves, when we do the mitzvot - that we acknowledge come from Hashem - but if out of imperfect, selfish motivations - to avoid punishment or to receive reward - do we serve Hashem? The Rabbis say one who serves for reward ultimately serves himself!! (Path of the Just ch.19; Shla HaKadosh). So on the conscious level - definitely higher one who knows is doing because Hashem commanded. On the other hand, on the motivation level, one who is driven by an unselfish, collective spirit, has an advantage over one driven by private, selfish, self-centered concerns (see Rav Kook, p. 84).
(2) (see Yerushalmi Brachot 1:1, that redemption comes little by little, in stages and Yehezkiel chapters 36 and 37 - that the physical revival and redemption come first and after that - and from that - the spiritual).
(3) Some sources that teach us to see the true inner source - and not be subordinate to the superficial, external facade of what is presently revealed.
--Rambam, Guide for the Perplexed II:45, delineates 11 levels of prophecy, the first, lowest, being Divine Inspiration where one is inspired to do something good, to save others (serving the nation of Israel and putting his life on the line). It is Hashem who infuses a spirit of courage - even if the recipient is not aware of the true source.
Amazingly we find that even the great prophet Shmuel was unaware of the Divine source calling him at the first stages of his prophecy!
--Tosafot Bava Metzia 106a defines the Divine asistance to a shepherd to protect the flock, a "minor miracle," as a spirit of might, courage, and the wisdom, know-how to fight.
(3a) -- Torah giants that saw the inner Divine hand as the source arousing the nation over 100 years ago, despite its being defined by the participants as a secular movement. The Netziv of Volzhin (in his letter supporting the Zionist revival, printed in Shivat Tzion II:7) writes that the fact that this movement encompasses the nation, different groups from different places, this in an indication that it does not emanate from a certain leader's charismatic influence or ideas of a certain group, a product of man-made concepts - or misconceptions, rather "the voice of the masses is the voice of Hashem." So too the great possek Rav Yeshua Kotna in his Yeshuot Malka (Yoreh Deah 66) points out that since this awakening includes all types of Jews, secular and religious, it stems from the collective Divine source of the Jewish people that transcends the individuals (and their explanations).
(4) This requires further study of the distinction between the objective, Divine, immutable essence and the external, subjective, human, conscious, behavioral level - and also the relationship between them. Just for opener see Maharal Netzach Yisrael Ch.11; Rav Kook Letter 555.