I can see that the other kids clearly are being exclusive and mean, then lying to her and to me about their behaviour I haven't got the FAINTEST idea how to deal with that without seeming like I am just taking my own child's side. And simply sending the other kids home doesn't seem like a good idea either.
Dittoing the suggestion for the Good Friends Are Hard to Find book. Just to give you a preview one of things he suggests is to focus on one on one playdates. It is much easier for kids to develop better social skills one on one. Anytime you start getting bigger groups there is more risk of exclusionary play and that sort of thing.
I didn't catch how old your child is, but with preschool or lower elementary kids... If you do have a group over my suggestion would be to start with a clear statement of the rules "At our house the rule is everyone gets to play" and then if you see violations of that rule remind them of the house rules and make it clear how it applies.
