Sweet Sam do you live in my neighbor hood?! You've discribed my living conditions to a tea! The children in this neighborhood are like stray animals. I left my front door open for just a moment while I was trying to attach a christmas bow to my banister and this little boy tried to wander into my home! He was old enough (I'd say 10) to know better than just to walk into someone elses house. They destroy my decorations (if they are in the ground they stomp on them) They try to get in the house, if that doesn't work they knock on the door and run. Its just annoying.
As for the little girl who did this to the doll... this is what I would do. I wouldn't tell the parents because they could make the situation a WHOLE lot worse... you do not know her situation at home... where the aggression is coming from (could she be abused?) etc. What I would do if I was your daughter is just not invite her back to my home. I wouldn't destroy a friendship over this, but I definatly wouldn't bring them willingly back into my own home. Constanty find excuses.. like why don't we go to a movie instead... or the mall, or sorry I'm not allowed guest over at the moment. If the girl finally catches on that she isn't welcome at your house... it will lead her to ask why not? Your daughter can just say kindly "Well, things always seem to get messed up when we are at my house so I'd rather we didn't go there." You don't have to point a finger or remind the girl of a particular situation. Unless she has serious mental issues she will understand, and the internal guilt will serve its purpose.
The problem with taking her into your home and letting her know that you forgive her gives some people, who have not had strong parental guidence, with the impression that what they did is ok.
Its kind of the old religious paradox of the killer who kills someone and then repents... then kills some one... repents again (continue for x amount of time)... the problem is that saying you are sorry and the whole forgiveness concept does not work unless you are truely sorry.
Will she be sorry? I really doubt it. I would have felt soo bad if it had been me who had done such travisties... but to suggest cutting the dolls hair... she was diliberatly trying to destroy the doll... it was not an accident or a misunderstanding because she hasn't had one of those dolls. The problem is figuring out WHY is she being destructive...
As sad as it is, what ever her problems might be, I do suggest keeping your distance in some way.