I'm gonna agree and disagree with the others right now. Yes he is still doing things that seem like he may want to be there. But he is also doing things that say he doesn't.
There comes a point, where you are going to have to stand up for yourself, even if you end up alone for a while, and say "if this is they way you are going to continue to treat me, then I am done". You do this for you. For you and your kids. It does not mean you are saying goodbye forever. You are showing him that his actions do have consequences and that you have enough love and respect for yourself to not allow him to mistreat you while he figures out what it is that he thinks he wants. He got himself into a situation that I'm pretty sure he did't want, wasn't looking for, didn't plan. But the result of that was a son who amazingly he cannot deny. Which I give him a lot of credit for. He tried for a long time to keep the secret, probably to protect you and the kids as well as himself. But since the reveal, he has been all over the map.
Honey, you have a lot on your plate right now. More than anyone should have at one time. IMO right now you have no choice but to focus on yourself right now. If it is what they say, it is not an immediate death sentence. You can still have a life and a good one but you have to remove stress and unhealthy habits. That is your responsibility right now, to do that for YOUR children. I don't think you will be able to do that and try to fight this unending confusing fight with him right now. I know you love him, I know you want him, but you also know what you have to do for you.
Be still if you must, but be still and see and hear what is going on around you and you will KNOW what you need to do. I think you already do, it just doesn't necessarily fit with what you want or what you should be able to have right now. LS is not slamming the door. It is taking a stand, it is telling him you are not a doormat and that is the bottom line. It says if you want to be with me, then you have to choose. If you don't do something, this behavior is going to continue indefinately and I know you don't want that either. Love you and you know I will support you whatever you do.
If you focus on the past, you ruin the future. You can only live for today.