What the fuck is wrong with people? Is it really out of the realms of your mindset that a girl of FOUR would have remembered what that woman said, and was able to repeat it back?! 
Some kids are bright, and girls are especially advanced. (Not saying boys are are not intelligent, just that girls are earlier learners.)
Like several other posters, I also remember a few nasty things said to me by certain people, from when I was 3 to 5 years old. And my daughter could count to 50 at the age of 3. So don't assume because your kids (or you) were not so advanced, that other peoples children are not.
I believe the girl AND the OP 100% because I have known jealous and bitchy new girlfriends SAY that kind of thing, because they can't bear it that the ex wife/ex girlfriend is still getting money from their man.
Well too fucking right she is, because they are HIS CHILDREN. He doesn't get to walk away from his responsibility, and his girlfriend needs to suck it up, or fuck off.
I would absolutely be telling my ex that our children are no longer going to be with him and HER unless supervised by a mediator, or with me there. And I would tell him why. And I also believe she has been dictating what the kids eat.
The new girlfriend sounds like a cunt.
I hope he knows what he has got himself into.
But yeah, quit the 'I don't believe the child said that' bollocks. So rude. 
Oh and yes the OP can intervene and stop this woman seeing her if she thinks the safety and welfare of the children are at risk. And it sounds that way, as the 'new girlfriend' sounds unhinged.