Translation:I prefer feeding the cat than feeding the children.
In American English, we would not use than with prefer. It would always be I prefer X to Y. I prefer feeding the cat to feeding the children.
I'm English and put "I prefer feeding the cat to the children" which is perfectly correct here, but does have a dual meaning — I could like the children less than I like feeding the cat, or I could like feeding the children less than I like feeding the cat!
Your version is what I would say in reality, but I didn't put the second "feeding" in my translation (which was marked as being wrong!), because it wasn't clear that the choice was between feeding the children and feeding the cat. :-)
That's what I put, too, and I think it was not accepted. Of course, I just added "feeding" to avoid the vagueness, or perhaps not vagueness, if your children are peckish for cat.