I haven't read through all the posts here, but I have a couple things to say.
First, at this point, I wouldn't go out of my way to say something to the family about the behavior of thier child. I would be honest though if they bring it up. You don't really don't konw what goes on in the home. Did she do this from watching Mom or Dad, watching TV or other kids she plays with? Or do the parents just lack the ability to dicipline when the kid misbehaves. Most kids will lie, cheat, steal and sometimes hit without being taught, but it's our job to teach them this is wrong. So who knows what she's learning.
I woulds say, I would not go out of my way for this family again. You can't put yourself or your kids on the line like that. They are just taking advantage of your hospitality and willingness to give. Don't bother anymore. That energy can go towards other things.
There is a good chance the friendship may be altered at this point anyway. Sounds to me like the little girl may have said a story to them.....
I had some freinds that we hung out with all the time. They had a son who was younger than my kids but he was ( and still is ) a tryrant. They never disciplined him ( and Mom's a teacher ), and he continued to do stuff. One day they needed me to watch him so I did. Well, this kid finally did me in....he threw an old metal cap gun at my son's head, narrowly missing his eye, but causing a big gash and an instant black eye. I took the toy away, and put him in time out in his room. To say the least, we don't hang out anymore, but I'm ok with that. Our daughters are best friends, and that's the only thing that makes it hard.
I hope it works out for you.