I don't necessarily agree with the idea that you're better off single, but one element that hasn't been mentioned is your boys (except with mention that they don't need a substitute mother). They will be affected if you enter into a relationship right now, and if it's up and down for you, it will be bad for them. If you got serious and they got attached and the relationship ends, it's bad times 3. Especially since you are essentially their only parent right now. And even if she's a bad or inadequate mother, it's still got to be a tremendous loss for them. It's not a bad idea to stay single and focus on them while they're still growing up.

(But I've never been a parent, so what do I know? Otoh, I have been a child for all of my life and know what it's like to be messed up by a parent.)