You need to go to the state department of social and health services. There is emergency assistance and there is help just for people with children. There are also organizations that can help (hopelink, etc), shelters, and even churches (you don't have to be religious to get help).
Talk to unemployment again about this and tell them the circumstances.
What your company did doesn't sound legal. if they offered you a permanent job and you'd signed all the required paperwork, etc...then they shouldn't be able to take it back and fire you or say that you've quit.
This is not a question. Go back to unemployment with the evidence of your situation. If you don't have any, it's because this story isn't 100% true. Do what you can in the meantime, don't make decisions that leave you stranded, and in the future save up so when **** hits the fan you can cope with it.
Lets everyone send a dollar. What is your name & address?
Have you tried porn?