This is really the only question. If she is willing to support you and accepts - after asking those hard questions, which she MUST do to cover herself - that you're doing fine, then stick with it. The very fact that the kids are all over you proves that you are offering them something special, so to deprive them because you can't cope with a false allegation is to be unfair to them. On the other hand, if your boss isn't willing to stand up for you to the parents, then you probably do need to move on.

But whatever you do don't rush into a decision; the kids love you - don't deprive them unless you need to. And what does it say about the parents that your input to their kids lives makes such a difference to them? This of course may be an element in the situation - you are generating guilt in them about the way they are looking after their kids, so rather than deal with that they shoot the messenger. Just make sure you know what the centre's rules are about appropriate touch and all those sorts of issues, so that there won't ever be an issue of your breaking the rules.