First question: Has kitten been to a vet? Some of the behavior could be caused by a medical issue. If that has been ruled out....

Second question: how old is the kitten? If under 12 or so weeks, it could be a litter training issue.

Are you looking for suggestions for helping the kitten stay in her home, or suggestions for how to find a new home?

If the former, the kitten has to have space that the kids aren't allowed.

If the latter, did the kitten come from a breeder? If so, most good breeders will take kittens back if they don't work out for any reason.

Maybe give a few more specifics, and I'll see if I have any ideas....