I have two big problems with this. Number 1 she is 16. The other is she has gotten out of an abusive relationship with a guy that sounds like he was also older. Sounds like a bad pattern on her part. She is immature and has some growing and healing to do. Plus the fact that she has parents that don't seem to have a clue if they don't care that their daughter gets involved with another older guy. This is bad news on a lot of levels.
You are 19 going to college, she does not need to be your summer fling. Find someone your own age. She is too young and vulnerable for you.
Tell her "you are a nice girl, but I dont think this is a good idea" and then leave her alone.