Baruch Hashem, a birth is expected in my family after I will have been in Israel for 6 months. My mother is expecting me to come back for that, and I don’t know what to do. I know that this does not fall under the 3 reasons for leaving Israel (business, learning Torah, finding a wife), but is Shlichut Mitzvah a possibility? Some Mitzvah that can be done that can help warrant the trip (especially if there is no Brit Milah to attend)?

I understand that by now you have made Aliyah and I hope that it is as painless and as rewarding as possible. It is permissible to travel outside of Israel even for the purpose of visiting with a friend (Magen Avraham 531,7; Mishna Berura 531, 1; their opinion that this is considered a “mitzva” is based on R’ma Orach Chayyim 249, 4); it is clearly allowed, therefore, to travel to participate in a family Simcha.