I wouldn't watch that programme in a million years!
I know a few people who agree with you on that, and there were a few postings online from people who said they wouldn't watch the show anymore after Sunday's episode. It's actually a very well-written show, very well acted.
As stupid as it sounds, in the context of the show, it was the right choice to make. The two adults had two children and a baby with them (none of them their biologically). They are heading to a town that is supposed to be a safe haven in the middle of a zombie apocolypse. The oldest child snaps, and kills her younger sister, and threatens to kill the baby.
In this world there are no detention centers, treatment centers or psychologists. Do you take this child with you hoping she doesn't snap again and kill others, or do you think of the safety of others (and yourself) and do something like the act I described above?