What boundaries are appropriate for my boyfriend's ex?

Today, I've made the realization that my boyfriends ex just WON'T go away. Ha-ha, my boyfriend (Lets just call him AL) and I have been together for almost 8months. He confessed that he was in love with me a few months ago and so far things are going great. I couldn’t be happier save for one problem. His ex.

She texts him several times a week and spam calls him. Meaning when he doesn’t answer his phone she calls back to back until he answers. Why? Just to talk or if she is having a problem with her new boyfriend general... I find this to be inappropriate behavior coming from an 'ex' who has moved on. She broke up with him 4or5 months before we started dating and continued to play mind games with him even after we became official. To be honest, I’m not sure if he has gotten closure or has fully moved on despite his reassurances. Maybe I’m just being insecure because Al explained to me that she is an ex for a reason and that’s the way it’ll stay. However, I still feel that she is overstepping her boundaries. My problem is not only that she is an ex, it is also all the mind games she played in the past. I can’t bring myself to trust her. Or trust him to turn her away. I guess my suspicions are getting the better of me...

She texted him a week or so ago: “I want you in my life.”--- “I love you as a best friend.” ---“You are the only one who ever understands me no matter who I am with.” --- “I’m just going to show up at your house.” --- “I need your help.” (Hopefully you can see why I feel a bit of jealousy.)

Al, on the other hand, doesn’t see a problem with her texts or calls. He says that I’d get jealous if it was any girl showing him attention (please keep in mind that I’ve only gotten jealous twice since we’ve been dating and that’s because a drunk girl kissed him at a dance) I guess its partially my fault because I gave him permission to be friends with her but this is getting to be too much. I told him that it really makes me uncomfortable but he refuses to cut ties with her using this “You said we could be friends” thing. I’m torn between the grown up thing to do (accept that she is a part of his life and work around it) and what makes me comfortable (him to stop all contact with her).

In fact, he’s set up a group date for the three of us because he wants to show me that there is nothing going on between them other than a platonic friendship. I don’t want to lose him but I’m just getting too uncomfortable with this. If I can’t find a medium there’s no choice but to end it. I’m losing too much sleep over this and all this anxiety is turning to depression. I guess my real question is how can I interact with her gracefully? Someone please help me figure out what are appropriate boundaries to set for this kind of situation.
What boundaries are appropriate for my boyfriend's ex?
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