Adoption is a legal process. If your boyfriend adopted his ex's child while they were married, your boyfriend is legally his parent, and as such, he has legal rights. The ex has no right to keep this child from your boyfriend just because they're now divorced because your boyfriend is legally the father.
That's not to say that bio dad may not have some rights (depends on your state and the terms of the adoption), but the ex should not be interfering with the relationship between your boyfriend and HIS SON! This is really, truly damaging to this innocent child.
Sounds like your boyfriend needs to be in closer contact with the lawyer and ask him/her specifically what can be done so that your boyfriend's time with his child is protected and how the child's best interests can be protected.
Children need stability and security. This little boy has had LOTS of changes in his tender 8 years. First bio dad leaves, then boyfriend becomes the legal dad, then parents split up, then dad gets a new girlfriend, then bio dad comes back into his life. Can you imagine what this does to the inner world of a child? Who'll be next to leave? Is it any wonder he "misbehaves?"
You sound like a kind and caring person, someone who really wants to help this little boy. Your boyfriend sounds like a good dad who wants to have a solid relationship with his son.
Have you and your boyfriend been together for some time? Are you living together? Have you talked about commitment and your long-term plan as a family? I don't ask to make any moral judgment, but if you are just the girlfriend for now, and there's no long-term commitment, that is not helpful to this poor child. For all he knows based on what's happened in his life, you could be gone next month with a new girlfriend in your place. I'm not saying that in any way against you and your boyfriend….it's just how kids look at it when there is a revolving door of boyfriends, girlfriends, and step-parents.
Your boyfriend's son didn't ask to have such a complicated family situation, but there he is, right in the middle of all of these adults who should be working together to see that HIS interests are protected and HIS needs are met. Family therapy will help you find ways to deal with the "misbehavior," which in a situation like this, is really not uncommon. Don't let the child become the scapegoat in this complicated adult relationship scenario. His "misbehavior" is telling you something.
Family therapy will also help you to find a way to communicate with the other adults in this child's life and develop strategies to get along or at least minimize conflict where the child is concerned. I know that it is not easy, but your boyfriend (and eventually, you, if you are going to someday be the step-mom) must do whatever is in your power to develop a cordial relationship with the bio mom and the bio dad, if he remains in the child's life. This cannot be overstated! You adults HAVE to find a way to work together in the best interests of this child. That's the job of the adults REGARDLESS of how they feel about each other.
Ask the court for help, and in the meantime, get with an experienced family therapist so that all of your energies can be focused on ensuring this little boy feels emotionally safe and secure and that the adults in his life truly have his back.