(i've never been married, and if society doesn't change, never will be, so my opinion my not be the most... experience based. but here's my speculation anyway.) From what my limited knowlege of marriage is, its a two way street. There usually isn't any one thing that one person can do to permanently dissolve a marriage. (you know, like if you went and killed all of your husband's friends and family, that may be grounds for divorce.)
Odds are, neglect wasn't the reason he divorced you... (or atleast all of it. you shouldn't take it all on yourself anyway. unless of course, you killed all of his friends and family. then definitely. take it all on yourself.) He may be afraid of commitment, who knows, but the worst mentality to take is "its all my fault...i didn't do enough". My mom's first husband was abusive, and that was the mentality she took (until her parents snapped her out of it). If he REALLY DOES NOT want to marry you, unfortunately there isn't much you can do about that, and its unfortunate that children are involved, but remember there are many, many fish in the sea. odds are that a few of them will be more than willing to settle down with you and your four kids.
(again. my speculation. i could be totally off here.)