I've been there! My son has a friend whose mother feels that "to discipline him would stifle his inner creativity." Oi. I loathe seeing this kid - and the sad part is that it's not his fault, it's hers. She's teaching him he can't do anything wrong and that it's okay to never apologize and he's going to learn the hard way that people don't like that!
It's easy to say to cut the friend off, but that is easier said than done and, if the friendship is valued, should be a last resort. I think there are ways to broach the subject of the little girl's behavior.
While the direct approach may be difficult, perhaps bring the subject up by asking her advice on disciplining your child in a separate situation (for instance during church, etc.). The conversation can then turn to comparing discipline strategies. This might give her some ideas - if her inaction has been fueled by not knowing what to do . . . She may realize there is a gap and begin to change her, and consequently her daughter's, behavior.
Another approach may be just stepping in and gently explaining to her daughter that something is against the rules in your house. Either the mother will let it slide and note that a behavior change is necessary, or she may take offense and speak to you about it, and if she does, it opens the door to explaining how you feel about her daughter's behavior. Be prepared to offer specific and recent examples of where you feel adult intervention is necessary, or how her daughter's behavior impacts your daughter's behavior.
Lastly, just speak to her directly, but prepare what you'll say in advance - avoid accusations. We mommies can get pretty defensive since our children's behavior reflects our parenting. (Or, at least it seems that way!) If things need clarity then tell her about how your friends were upset at your daughter's party. Explain that they were upset by the little girl's behavior and that you want to include her daughter in parties, etc. but don't want your other friends and their children to cancel because of her daughter. Nor do you want to exclude her daughter. It'll be a last resort, but I've often been of the opinion that there are times when you sacrifice friendship for the greater good. That being your child's good!
Good luck!
-A.