If there is a possibility that she will move out in 2 weeks, then wait and see if that happens. His behavior is not so much more indicative of him not communicating with you than it is a sign of his poor boundaries. If you feel disrespected or uneasy about this living arrangement that he has with her, then he will need to correct it. He is also enabling his ex saying she has nowhere else to go. She is an adult and need to find ways to live with someone other than her ex.
You've waited for about 8 months for things to change and they have not. You love him and are giving him a chance and at some point sooner than later, he has to resolve this issue. As far as whether or not you should leave him, it is something no one ought to tell you what to do. You've got to decide if this is working out for you or not, and how much longer can you compromise it.