Yes-- it IS dangerous for your DD.
It's relational aggression and the aggressor sounds highly manipulative and downright toxic, frankly.
Do I have to let someone be in my house who lies and breaks our rules and freaks out DD just because that someone is a relative?? And do I have the "right" to think my sis is a weenie because she blames everything on my daughter, says I baby her, she's too sensitive, etc. I am only talking about incidents that my husband or I have directly witnessed, so it isn't a "she said, she said" situation.
If it were someone PHYSICALLY harming your DD, what would you be thinking?
Honestly, I think that your sis is enabling budding abuser of a kid. Unvarnished, but there it is.
Have you asked your DD what
she would prefer? She may prefer to meet on neutral territory (local park/restaurant, etc) so that your family has a way to escape the behavior when it gets out of hand.
I don't know what your relationship is with your sibling, but perhaps it would help if your DH intervened here and told her that she MUST control her child's behavior while at your home-- or your hospitality isn't extended to the offender. She's ignoring your stated "house rules." Your sister, at least, is not confused-- she's disrespectful of you as adults and she's being pretty darned passive-aggressive about it. I can't quite understand actually being able to have them back over after listening to a family member TRASH the parenting/child of the host. I'd insist on an apology and genuine repentance first, but that is me.
Some of this may explain, actually, why we don't have a lot of close relationships with family-- we ARE willing to forgo toxic contact like this. Can't say that our way is for everyone, certainly, but it definitely communicates to our DD that she should NOT tolerate abusive conduct from others.