I also believe in love, and in standing by those you care about through difficult times. But it has to be a two-way street - a mutual exchange of caring and support.
Sorry if this sounds harsh, but what exactly does he contribute to the marriage?
You've described a man who is OK with you supporting him, who is apparently oblivious to your understandable exhaustion (so much so that he talks about how tired he is after YOU come home from a full day's work), who not only shows no interest in being a father to your sons but, in the incident with the food, puts his needs/desires ahead of theirs (BTW this is not adult behaviour), and who physically leaves the house or "fades out" regularly with his drinking.
Whatever his qualities may be as an individual, he does not sound ready or able to be a partner to you; so the unconditional love you are giving him is more like a parent's love for their child, rather than a wife's love for her (equally contributing) partner. Is that what you want?
You sound like a strong, courageous person who not only managed to build a new life after being dealt a devastating blow, but also managed to stay positive and keep believing in love. I think that's a good thing as long as your idea of what love looks like/feels like is healthy. You say your husband is "not controlling, he doesn't look at other women, he's basically a nice guy, nicer than I had ever known." Is it possible, given your previous experience, that your expectations are too low? Should a man really get credit for NOT being controlling or cheating?
I too am a caretaker, and I also tried to love an alcoholic husband out of his illness for years. For a long time I managed to ignore the problems by focusing on the "good stuff" - he was intelligent, funny, he occasionally helped with the laundry... After a while none of that outweighed the fact that he was less and less present in the relationship. His primary focus was alcohol. And even when I realized that, I clung on for a while longer because I refused to abandon him, and you know, it could be worse - he didn't hit me like some alcoholics do; he didn't cheat, crash the car, etc.
Looking back I recognize this as insanity. No-one can heal another person - they have to do that for themselves. And talking about recovery means nothing - it's all about ACTION.
Here are a couple of things people on this board told me when I first shared my story, that may be useful to you:
"Consistently being under the influence while married and expecting the marriage to be treated like it's a sacred relationship is not merely rude and disrespectful, it's delusional."
And even more importantly,
"This is your life too.
Your life matters.
Your happiness is important."