Having a hard time with my boyfriend being "friends" with his ex?

[Sarah]

My boyfriend and I have known each other for 10 years and have been together since January of this year. We moved in together in June. We get along amazingly for the most part but he is still friends with his ex that he lived with for the past 6 years. I have asked him to please stop talking to her but he is constantly posting things on her facebook page and talking to her on messenger on FB. Last week he posted a .gif from an episode of 30 Rock from an episode entitled "Let's stay together" and it was a clip called "Jenna Maroney, Master of seduction" and has the female wrapping her leg around a guys shoulder. About a month ago when I was at work, my mother went by my house to drop something off and caught the ex g/f in my house with him. When I questioned him about it he said that she came by to see the dog they used to have together (who now lives with us). I'm not buying that. My mom sat outside the house to make sure she left and she called me a few minutes later telling me they left together with the dog. He never would tell me where they went other than "to walk the dog". He says that I am trying to be controlling in telling him who he can and can't be friends with, but I don't think he needs to be talking to his ex. Am I wrong? I don't talk to any of my ex's. Another thing is he is currently unemployed and I work 12 hour night shifts, so I am paying for everything. Am I in the wrong here in this situation? Is he being shady and do I have the right to be suspicious about him talking to her, or am I really controlling? What do you people think about my situation?
she also recently changed her facebook profile picture to their dog, who as I said now lives with me. I feel like something is up or either she is trying to piss me off.

[A.]

Umm.. No. He should respect you enough to stop talking to his ex for you. You aren't being controlling at all. You're his girlfriend, it should be YOU before anybody else. Tell him straight up what's expected. That's just not okay. Confront him. She's an ex for a reason, so she should be cut as of now.

[L]

Kick him out!!! Don't allow him to treat you that way!!! He's using you since you're paying for everything !!!