I've been both a single mum (on my own without support) and a divorced single mum, on my own with support.
Here are some of the things that helped me to get by and build a life.
First, there are *many* government and social agencies that are there to assist you, but you have to knock on their doors. Women's resource centers, shelters, county and state offices, etc., all have programs available. Here are a few that I'd found.
First of all, I *worked*. People don't mind helping you when you're trying. I worked full time and did the best I could every day. There is nothing ever to be ashamed of in seeking help when you're doing your best.
I found daycare assistance through county offices. Because of my income my daycare was a fraction of what it would have cost without subsidy.
Housing assistance. Through the women's resource center I found a program that led me into subsidized housing within 2 months (the waiting list was 3 years) and a 2 bedroom apartment cost (((drumroll)))) me $64. per month (based on my at the time, minimium wage income).
Through another county program I found assistance to buy a car.
Through a state program I found heating assistance, Food stamps, and medical assistance. These all supplemented my insufficient full time work income.
When I was divorced, I never left anything to chance. I did have a lawyer, and I did pursue child support. It wasn't much, but I insisted it be garnished from his wages. When ex and his new wife attempted to get a reduction, I countered with a request for a full review and the court almost doubled it. (Boneheads).

I was fortunate that my employment was with a college. I was able to go to school there free and I did. I graduated Summa Cum Laude and then pursued a second degree elsewhere. I've put both my kids through school there. I've built an excellent resume and a good future.
A college is a great place to seek employment.
I would highly recommend if you haven't obtained an education do everything you can to go for it now. Go to your local community college and check into degree and training programs. Assistance is available for those who are struggling financially, and sometimes the best time to grab the world by the tail is when you're struggling. Be agressive in pursuit of your new life.
One thing I can say I found to be true, is expect nothing from your ex and you'll never be disappointed. Get a good lawyer, go for all you and your children are rightfully entitled to and nothing more. Stay on the high road even when you're itching to jump in the mud. Then be resourceful. Work. Knock on doors. Have courage and do your best. And please, please protect your children in every way you can from power struggles between you and your ex. Those can be devastating, and their effects can last a lifetime. I know because I too am a child of divorce.
God bless and Good luck,
Jo