I'm not sure this sounds like something that you can just forget.
It sounds like he made some big mistakes, including some behaviour that is never acceptable. He has now apologised, I presume, and he is invested in making things better.
But if he wasn't there when you needed him, if he proved himself unreliable when you were at your most vulnerable, then you won't be able to magic away those feelings. He doesn't really get a second chance at that. Your brain learns who you can rely on and who you can't, and if he wasn't there in the moment, it'll be a very long, difficult road of being able to trust him again. It makes sense that your head can't just forgive and forget, that it feels let down. It's self-preservation. It's reminding you that you shouldn't fall into a false sense of security, that you can't rely on him.
So first you have to work out whether you can. And then you have to convince your brain of that. CBT or therapy might help, but as you said, you've seen a therapist and she felt it was a normal reaction as well. Therapy won't convince your head to trust him. It can't. It can't override those natural, normal instincts.
Relationship therapy might be able to teach you ways to build a bond. It might give you somewhere to talk, and try and be productive. But again, it can't replicate that situation of needing him.
I guess my point is that you can't change the past, and so you can't convince yourself that he'd be there for you if the going got really tough again. You can learn to live with things how they are, and you can forgive him, but you can't change what he did and how your brain has responded to that, and if you can accept that your brain is just doing what it was biologically designed to do, that it's just keeping you going, you might be a little less frustrated and angry with yourself. You're blaming yourself a lot.
Is there any way that you can forge a new connection? Could you do date nights, in any sense? You need to find a way to connect and to fall in love again. You need to recreate the trust that you lost, and find a way to reboot the relationship and lose the pain and hurt. With young children, that will be tough, but it has to be a priority.