"Who is the father of your children?"
Translation:Kdo je otec tvých dětí?
We use "svůj" when the grammatical object belongs to the grammatical subject. In this sentence, the children (object) belong the person we are talking to, but she is not the subject of the sentence.
If you say: "Kdo je otcem svých dětí?" it would mean something like: "Who is a father of their own children?" ...Well, the answer for this would be that every man, who has children, is the father of these children :-D.
Ok, I hope it is at least a little understandable and you didn't get even more confused.