Jay2 and Scout have hit the nail on the head. You need to work on it together, and he needs to look at a different approach, even if it means a less-than-standard job for a little while.
My husband is a professional adjunct professor and trainer- NOBODY has made money at it as he has. What most people consider a little income supplement, or a lackluster position paying less than $20K a year, he is building into a good business.
When he started doing it, he wouldn’t listen to one word I said, even though I was supposed to be his “partner” as well as his wife. He was fearful of networking, and he was reluctant to put himself forward or talk about his accomplishments. He made some blunders, which effected us ecomonically (

one is known as “The Summer of Rice and Beans”).
He had to get over his fears. He also had to realize the work wasn’t going to come walking through the door, but that he had to go out and get it. He attended workshops, conventions, and seminars dealing with entrepeneurship as well as training and philosophy (his area). He used email to just say “hi” to people and reminded them of when they met him and where, started asking questions about them as people as well as whether or not they had an opening for a seminar or a leftover class he could fill. He made business cards on the computer and put them EVERYWHERE. We have a web site with a domain name and email that has a domain name “alias”.
He’s gone from being this introverted, sloppily dressed, teacher-type guy to having some confidence. He has some sense as to when it’s appropriate to tell people about his accomplishments and not have it be just a brag but fact. He’s not afraid to contact vendors months before events or classes start, because he’s figured out when they plan their schedules. He has even learned how to appropriately “corporate gift”.
We’re still working on the clothing issue.
I had to stand back and let him make some hideous mistakes. I also had to say, “I told you so- now then, how do we fix this” with a measure of kindness. And I’ve had to let him schlep at some awful jobs for a month or two after he’d made a blunder. Funny, he’s always more receptive after one of those episodes.
I don’t know if telling you all this helps. I do know that things WILL change, but you can only change you.
You don’t let things go. You don’t let your kids go hungry. Marriage is an interdependence, not a dependence. If he isn’t doing anything, why can’t he take care of the kids while you find a part time job, until he finds something? There is nothing wrong with a dad taking care of the kids. My husband helps me with our granddaughters. He is their grandfather, and going to be their father. He can brush hair and drive carpool with the best of them, and does.
You might also have him checked for depression, if you can afford it.