If you put her on probation my experience tells me the parents will go and find alternate care. I mean, really, it's not like they don't kNOW she is like this. And the fact that they are aware of her behaviour but not addressing it says that they don't see it as a problem. So your putting her on probation is just going to tick them off and make them defensive. They WILL leave if you put her on probation. But, hey, would that be so bad?
Personally, I think you have put up with enough for long enough a period of time. It's time to just let her go.