Translation:Why do you think that I have bad children?
Would this mean "What makes you say I have bad children?", "What do you think is the cause that I have bad children?", or both?
Yes, it's not clear whether these interpretations are both there in just the English or also in the Russian
I think it's because it's correct in meaning but the russian sentense contains что which means "that". Not important for the meaning in english but closer to the original russian sentense when you include it. Just to say it: I'm neither native english nor russian speaker so all I am saying is what I think was the problem that duo had with your translation :)