So sorry you're going through this op. It sounds so familiar to my situation with DP and his behaviour, though we are a few months down the line.
I have felt the lowest I have ever felt in my life. Now, I am starting to feel a bit better when I couldn't even imagine that happening a few months previously. You will feel stronger in time, look after yourself, focus on you and the kids, cry, be angry, feel all the horrid shitty feelings, it is part of the process I'm afraid.
I wanted to work on things too but DP didn't, we had the long emotional talks, the counselling, me trying to convince him to try. No point to any of it. If they want to work on things they will, if they don't they won't. I do believe it really is as simple as that.
Don't chase him, I know you don't want to give him space, your instincts are probably fighting to do whatever you can to keep your family together (I know mine were), but there's no much else you can do. Give him all the damn space he wants, he doesn't deserve to be around you and the kids anyway. Don't wait around for him, if he came back wouldn't you just be waiting for the next time he gives up and walks? Don't be his back up, you're worth so much more.
I'm still convinced mine is having an affair or had someone lined up. He swears blind this isn't the case but his behaviour has shown me not to trust a single word he says anymore and I don't even recognise him anymore. I'm pretty sure that is what's going on, I feel it in my gut. Even his mum thinks the same. He won't admit it though because he will look like an even bigger piece of shit than he already does for walking away from his family.
Look after yourself 💐