What you should do is slow down. Eight months is a very short time to make a lifetime decision. You may think your marriage was over long ago but you haven’t been divorced. Please take the time to make sense of your prior relationship and what went wrong. You’ll be sharing parenting even if you aren’t sharing a life together so it’s important to gain perspective and, hopefully, a positive working relationship with your ex.
Your boyfriend seems to want you to have no past. That’s unrealistic and unfair. To be with you is to be with someone who has had a life that was different from his own. He’s right that he will always be on the outside to some extent. That’s not the problem. The problem is that he can’t accept that fact as your reality. You have two little boys who ideally should have a relationship with their father. They can also have a relationship with a stepdad, of course. But it’s unfair of your boyfriend to ask you and the boys to act as if the other man isn’t still an important person in the life of your family.
I very much hope your boyfriend is in active treatment for his depression. He needs to be doing the hard work involved in learning to manage a mental illness, not asking you to change your history to make it easier for him.
I wish you well.