Is it possible that she was molested?? A lot of girl's that are molested at a young age are very boy crazy because they equate sexual attention as being wanted and being loved
If her dad talks to her "weekly" - he isn't prevalent in her life, sadly. He's a shadow figure that she may think about all the time, but he isn't there. This is kind of typical of girls who long for their dads but don't actually have them - they replace them with boyfriends.
Is there some reason her dad is unavailable for her to actually live with?
Best wishes. I think you're doing the right thing by keeping her during the summer.
It also sounds like she could use a sport - volleyball, softball, tennis, soccer, etc., that she can be proud of achieving in and burn off some of that energy.
Sounds like she is dealing with a lot of insecurity about her desirability. Hopefully, she won't turn to sex when she's older as a mistaken way to bolster her self esteem. Her parents' divorce and her mother's multiple partners may be contributory. Finding healthy outlets, discussing values and giving her the opportunity to discuss and address her insecurity would be important. Will she open up to you about her feelings about all of this? She might benefit from counseling, perhaps a group for children of divorce. Good luck.