L.C.
Hi L.,
Wow, I think we have all been in this situation and it's a tough call. It's like taking on the responsibility of mothering someone else's child. Not only is it a huge responsibility, but a thankless one, and it may even make the other mom mad. Talking to her about it at all will definitely make her mad and further alienate the little girl.
It sounds like she is completely ill equipped to handle social situations. Even as an only child if her mom were up to the task, she would have social skills in place by now, but if she started school without them, it is really hard to catch up, and kids don't forget.
If you wanted to take her on and help her, I think that is a really good and noble thing; and while it may be thankless now, she will always remember you as someone who invested in her and she will be better for it. One day, she may do for someone else what you did for her.
At my house, the rules are the rules for any kid that enters. If they break the rule there is a consequence. If they don't want to deal with the consequence the other choice is to go home. I never put my hands on another persons child. But, for instance, not being a good sport means not playing the game. Running in the house means sitting down. Hurting someone else means being seperated for a time. In giving her boundaries you are going to teach her the social rules that she needs to know about what is acceptable and what isn't. You will also be staying consistent with your own kids. My friend even goes a step further. If kids are going to be riding bikes at or two her house, she goes to the library and gets bike safety videos and makes the kids watch them before they can ride a bike at or to her house again. I would also have activities that are planned to do when she is there so it is not so self directed. She seems to have trouble making choices when she is left on her own. When she comes over say something like, "We are playing with playdough now, and you can play if you want to do playdough." It also helps because then when she comes over unexpectedly you will already have things in hand.
She will care that someone cares enough to guide her.
Hope this helps.