My husband’s father was tragically killed in a traffic accident several years ago. When we have children iy"h we would like to give our first son my father-in-law’s name. Is it permissible for us to name a child after someone who died from unnatural causes?

It's permissible. Nevertheless – the common custom is not to give someone a name after a person that had a bad life, was killed, died young etc. since the name has an effect on the person who carries it. This custom is based on the Sefer Chassidim (244) and was copied by many Poskim. You can always add a second name or change the name a little from the original. My rabbi used to say based on the Talmud (Psachim 110 b) – if you are not concerned it does not concern you.