I agree with your pediatrician that it's most certainly bullying. And in your place, I'd immediately sit down with your DD7 and explain that, while I appreciate her efforts to try to help, that's an adult responsibility, and she's 7, so please don't.
And then I would have a conversation with the sister, where if she can't ensure her DD follows the rules of this house while she's guesting here, she can always stay somewhere else.
I know this can be hard where there are ties to family members and perceived responsibilities with that, but it helps to remember that your responsibility to your own DD is superior to that of a niece or sister.
I've had to end a really good friendship because of bullying behavior of his child towards my own, and the enabling behavior of the mom.
