Birth mother is driving me crazy

I have adopted 2 young girls, currently 10 and 6. I have had them both for almost 6 yrs, adoptions finalized last year. They were removed for neglect and abuse, and bio mom is an addict. We have continued to keep in touch with the birth mother (visiting at least once a month), and frankly I want out. But I also want what's best for my children. They say they want to see her, but usually only after a "phone call". If we don't hear from her, they don't ask to see her. If we don't initiate contact first, weeks will go by that we don't hear from her. Of course, if we've been seeing her regulary for a while, the girls want to know why she's not calling them or asking to see them. Eventually they stop asking. When she finally remembers they exist and calls and asks to see them, the cycle starts all over again. Recently I found out she had been taking photos of them I was unaware of, and posting them all over her Facebook (which I had SPECIFICALLY asked her NOT to do) about how much she loved her daughters and what a happy family they were together. When I told her to remove them, she ignored me, and blocked me from her profile. I had to have Facebook remove them. We hadn't heard from her for almost 2 months. I almost felt a sense of relief she was gone, and other than mentioning her name on occasion, they never asked to see her or talk to her. Last night, she wanted to talk to them. Right away it was "I miss you, I'm so sorry I haven't called you. My phone was stolen, I lost your number, yada yada yada. Ask your "other mom" when I get to see you again. Are you so excited to I'm giving you a new baby sister? Your baby brother misses you" I'm so fed up with the lies and the drama. To my face she's sweet as pie, and behind my back she's vicious. I feel like I constantly have to watch her because I can't trust her to be alone with them for fear of what she's going to do/say to them. I hate this feeling. It also bothers me that my oldest can't see my family as her family. We're not her family, we just adopted her. Her birth family is her family. Which is odd, considering she has never actually lived with them. She was taken in by an aunt (who passed away which is why I have her) as an infant and grew up with her family. I can't help but feel if they just went away, we would be able to move forward and this disconnect would go away. On the other hand, I dont' want them to resent me for taking them away. I don't want them to grow up without their "history". But I'm sick and tired of having to put on a happy face and be gracious and sociable with a a family I neither like, trust nor respect. Help!!