Hi....I'm also from Michigan. Go to this website and take action. There is all sorts of help available to you. It's a plus that you are a single parent with such young children. Since you live in Michigan, I know if you apply for State benefits, you won't be required to fullfil the work plus requirements until your children are school age (6). Go to this website and apply today!
http://www.govbenefits.gov/govbenefits_en.portal?_nfpb=true&_pageLabel=gbcc_page_benefits&_nfls=false
Also Google HUD, it's a housing benefits program that can help with housing and rent payments.
There are also benefits for help with heating and utilities. Don't worry....you should be eligible for help if you aren't earning enough to get buy whether on unemployment or not.
God Bless