"He is a teacher in my college."
Why is there a 的 between 大学 and 老师 but no 的 between 我 and 大学? Is this arbitrary? Would 他是我的大学老师 also be correct? (Duolingo marks it as wrong)
他是我大学的老师 = He is my college teacher, right? Would 他在我的大学(里)是老师 be a better translation?
他是我大学的老师: "He is a teacher at/in my college"
Your translation, 他在我的大学(里)是老师 sounds a bit off. As in it's not the normal way people would talk. It sounds like an answer to the theoretical question "What is his position at your college"
Alternatively, you could use 当 instead of 是, where the former means something among the lines of "to be in the position of (CEO, teacher, etc. for example)"
edit: Neither of your sentences is wrong per se, in the end it just comes down to small subtleties