I'm sorry you are going through a tough time.
Reality is.... No one pays you to stay home with your children. If they did, no one would be working outside the home! We'd all be collecting pay checks fur watching our own children. I don't mean that in a snarky way but think about if!
All the direct sales/mlm/and pyramids will hit on this post to sign you up to get rich quick. Again... Keep your head in reality!!!
Working from home is work. People who do work from home are required in most cases to have child care. Most people who work from home have been steady employees as well because it takes a strong self discipline and self motivation to make it work.
I do work from home but its a company that we founded and own. There's no way I could do my job with children around. One mistake can cost our company and personal finances thousands of dollars. I have an 18 yr old daughter and I still don't do my job unless I have the time to be in my quiet office.
Think outside the box. You say you " can't " babysit? Why? Why can't you turn that into an I can! Look at temp agencies in your area that have jobs along the bus line, look at working in a day care facility with your children.
How old are you? What are you good at? Can you teach how to play a musical instrument? Tutor students after school ( around here a solid academic tutor gets $50+ an hour) .
Talk to your previous employer. Ask if they can help with transportation or give you some options.
Best wishes to you and I do hope you find something productive for you and your children.