You’re right. He isn’t moving forward. By keeping the two families separate, he is preventing the “blending” that happens when people with children move from “dating” to making a new kind of family.
You and your ex have moved past your hurt and anger and have an amicable relationship. When this can happen, it’s best for everyone. The children aren’t conflicted about spending time with either parent. The parents aren’t still living in old pain. This is what it means to move on. Three years after the breakup, your boyfriend isn’t on speaking terms with his ex’s partner. It appears he was so hurt by the breakup of his marriage that he can’t take the risk to start again.
That’s sad. Your relationship sounds like it has promise. All you can do is try to talk to him about it. In a way, he is letting his “controlling” ex still control how he lives his life. His reaction to her behavior is holding him back.
He might find it useful to talk to a therapist to help him resolve his feelings about his prior marriage and divorce. Another route to go would be for the two of you to see a couples therapist – together – to help you find ways to reassure him and to help him trust you and your relationship as being different from him first marriage.
I wish you well.