I'm so sorry that you find yourself in this situation. If I may be so bold, the stepdaughter is just an excuse not to take control of your life immediately. You're grasping at straws, which is fine, but if this is the case, be honest with yourself.
If you're really hoping that the next 8 weeks will turn him around, then acknowledge that. Are you doing it for him - for the SD?
Maybe, if you walk away now, he'll be forced to spend time with his daughter and bond with her - it could be the best thing that has happened to them.
Your relationship with him sounds tenuous at best. Do you have any plans to marry - any commitment in the future? Or will he continue to pretend that he is single and sometimes has his child for visitation.
Good luck - I've seen this dance before.