I'm 10 years younger than you and thankfully my son is healthy, but I understand what you mean when you say, "how do I turn this around and find a way to love him again for the sake of our daughter?" my husband & I have gone through hell the past year, which was simultaneously the first year of my son's life and the first year of our marriage (we dated 4 years prior).
The answer is, you may not be able to, but there's another part to that question, and that is, what is he GOING TO DO to make you love him again? Do you really not love him at all? I had to do this very, very recently. Many lies and broken promises into a short marriage and I had to (and honestly am still) evaluating whether I can love my husband the way I used to. Of course, with a sick child, it's a different story, but I would guess that he feels your emotions radiating from you, and that WILL make guys more of, well, assholes. Ironically, most men become meaner as a response to feelings like ours, instead of trying to be nicer and kinder, thus making us feel more positive about them/us. IDK if your man is like that, but if he is... consider how your feelings are maybe making him act worse. NOT SAYING it's your fault. You feel how you feel. But you need to talk with him about it.
At one point recently my husband asked me if I even loved him anymore, and I could tell if I said no (which I do, of course, still love him) he would be heartbroken. Sometimes, it takes a course of conversation that serious to make them realize.... I wish I could offer more advice. About him lying about his job searches - I'd be mad, but I understand, too. As a guy, he feels like the $$ is his responsibility primarily. I don't care how much society has changed - men haven't. They (OK, some of them) have an ingrained sense of responsibility to their families, and when they can't live up to that, they lie, they cheat, they act mean... it's not right, but maybe you can reassure him in some way. NO ONE can find a job right now!!
Although it's telling that he doesn't attend counseling anymore - my husband promised to go and still has yet to uphold that promise, so I get it - it doesn't mean he doesn't care. He just cares differently. Maybe neither of you were getting much out of it? So maybe, find a new counselor.