Hi J T:
First off, you have to make yourself believe that you can do it. You obviously have drive and ambition, given that you have a degree and are raising two children on your own! Babysitting and cleaning tells me that you will do whatever it takes to take care of your family.
That being said, I was also a single mom for 6 1/2 years - without a degree. I had a decent apartment in a good neighborhood, a brand new car and a job paying $15.00/hr. We didn't have luxuries, like cable t.v., or a home phone b/c I used my cell. I only bought what was on sale; groceries and clothing. I had garage sales, and brought my son's clothes to consignment stores to re-sell. We didn't get to go to movies most of the time, or do all the costly fun things, but, we did make it!
I hope your 5 year old is starting school in the fall? If so, that's when you should pounce on job hunting. You may end up having to put your kids into a before and after school program (the YMCA has them at some schools and they aren't very pricey). Can the childrens' grandparents help a little towards this cost? Don't feel ashamed to ask your ex's parents for money for something like this. They can even make their check payable to the program so that they aren't actually giving 'you' money. They and/or your parents should hopefully see that you are trying to get out of a hole. This could probably only be a temporary situation until you start making some money.
Having a degree, you will be able to get a decent paying job and get ahead of the game in no time.
Good luck to you and your family. You truly sound like a supermom!