I'm so sorry to hear this. I read your first post and thought, Wow, I could have written that. My DH is very bad about birthdays and any other kind of special occasion. I feel like I am lucky sometimes to get even an acknowledgement of a special ocassion like a birthday or mothers day, much less a card or present. He has gotten better over the years but is still very bad. We have been together 24 years and that is one of my major complaints, but I learned a long time ago that it isn't because he doesn't care or love me. I try very hard not to take it personally because I know it isn't a reflection of how he feels.
What your guy has done is inexcusable to a degree, and I really couldn't blame you if you didn't let him come back. He needs to understand that although you love him, when people do things like this to hurt us, it causes us to put up defenses to protect ourselves. It causes a bit of mis-trust of feelings, and he will have to understand that it may take you a bit to let your guard back down.
He has broken down the trust not by cheating but by hurting you, and he needs to understand that you also will need time now that he has pushed it this far ecspecially without a reasonable explanation. I'm bored is not reasonable, nor is it a real explanation.
We tend to expect others to make us happy rather than take on that responsiblity ourselves, and he and you need to understand that our happiness and completeness for lack of a better word are our own responsibility.
I'm sorry, I didn't mean to get off on a tangent and sorry for the long post. I just feel so badly for you.
I think I would tell him next time he told me he's just bored, that he better be able to come up with something better than that if he expects you to ever trust him again, or will allow him to come back. You have a responsibility to your boys and he didn't hurt you alone when he pulled this stunt.