"Which one is yours?"
Not always, apparently. For example, "Neden üzgünsün?" is the correct translation of "Why are you sad?" according to Google Translate. Also consider "Kim tavuk yer?" ("Who eats chicken?") Regarding why "senin hangisi?" isn't correct, does AlexinNotTurkey's explanation that "hangisi" is a noun-like word shed any light? In my limited experience, questions using "hangi" generally have it at the beginning. Also, as language learners, I think it's sometimes best to accept constructs in our language of interest as we encounter them and trust that a deeper understanding of why they are the way they are may come later : )