Jo, Your situation really interests me for many reasons. I would like to say that you and Andy have been doing this dance for many years. I think that "you" are the stronger one of the two of you and it will only stop when "you" decide you're tired of the game. I see it as "he will only want you when you don't want him." He uses the girls to control you which I find totally selfish and repulsive. I'm sorry to say this. Instead of expending so much energy on getting him back, I would use it to find a legal and fairer way to be with my girls more. That's just me.
On another note, your patience, willingness to forgive and kindness are overwhelming. I hope that someday you get everything you have coming to you because you are an amazing woman.