it's good to see good in everyone and potential but that potential is many times never fulfilled because the other person is never motivated to reach it. By not doing anything to stop the abuse of her child for one (reporting her) and hoping she will 'get better' it's not only magical thinking, it's also enabling her to continue on the path to destruction. it's great that you can see past her faults but these behaviors are not only affecting you but a child who is dependent on her for protection and security.

The fact that she put her 10 yr old, defenseless child out at midnight says to me that she is a dangerously abusive person and does not deserve to have her child let alone be in a relationship with a caring man.

that you do NOT need therapy, I question it because your attachment and your hanging onto the idea that she'll get better is clearly unhealthy and you should want to find out the roots to why you want to hang on such a bad relationship.