I had the same problem. I earn about $15K a year and live in pricey So Cal. Fortunately, with my share of the equity of the family home, I was able to purchase a nice mobile home in a quiet family park in a great neighborhood. I have more space than an apartment and only pay $650 in space rent, which is cheaper than even a studio apartment out here.
You may also qualify for food stamps, welfare, discount lunches for the kids at school, free or low cost daycare and free health insurance. Don't be afraid or too proud to get help from the state... that's what it's there for. Look in your phone book or online for the appropriate agencies
Also, even if your ex is out of work, the courts determine child support based on how much he WOULD be earning, not how much he currently makes, and he can't get out of that.
Investigate all your options, make a plan, and then have faith that you and your kids will be fine. Look how much you've accomplished already! You supported the family when he was out of work, and kept things afloat... you can definitely do this without him getting in the way and brining things down. Trust that you will find a way, and then just DO it! You'll be surprised how easy it is once you do.
Fear kept me in my marriage four years longer than I should have been.... now that I'm out, I may struggle a bit sometimes, but for the most part all my bills get paid, my credit is great, and I have a roof over our heads, food in the pantry and a working car. Just do some research, find out what all your options are and make a plan that works best for you.
Some places to look:
Legal Aid society (free or low cost legal advice)
Your local courthouse (often offers free legal clinics as well as referrals to local agencies)
Your local social services department (welfare, food stamps, section 8, job assistance)
Local charities (low cost housing, furniture, housewares and clothing)
Your local hospital, health care center or city services department (often offer free classes or referrals to local agencies or charities)
City, county and state websites offer lots of information and links to agencies that can help!