Did it never occur to Slim to go a battered women's shelter?
Also, why does Mitch desire Slim to remain with him at all? Clearly he only values women for sex, and he gets that from multiple mistresses.
This troper got the gist that Mitch always wanted to be in full control. Remember that scene where Mitch seemingly saves Slim from that grabby customer. Fast forward some scenes later, you find out that the guy is actually crooked cop Mitch is paying off. Even though it is pretty ridiculous, it showed that he wanted full control from the beginning. Mitch only wanted her because he saw her as a possession and nothing more.
There's also the fact that killing him seems to be the only solution. Beating him up delivers a delicious dish of revenge but after that bit of fun surely there are other means (legal or illegal) of taking him of the picture properly. Methods that don't risk her child growing up without any parents her whole life with one in the ground and one serving a life sentence. If the cops weren't so useless that would have been a very likely outcome of her actions.
Actually, if you listen to the police that arrived at the end of the movie, he states that she is "One of the lucky ones". What this means exactly is anyone's guess, but this troper thinks that Mitch may have killed other women who realized what he was and tried to run from him. She's the one that fought back, and won. He's also the worst type of offender for a prosecutor to go after, one with ALLOT of money, so she did them a favor.
As for not going to a shelter, she probably feared (correctly) that it wouldn't take him long to find her there (remember how we soon see that he has connections everywhere).
Not that we ever get to see how come he's so ridiculously well-connected, mind you...