Thank you for your honest letter; I'm sure many people could echo it. Single mothers in particular have a very difficult life after divorce, and I want to assure you that God knows your situation, and He cares about you and your family.
One of the strongest statements in the entire Bible is found in the Old Testament: "'I hate divorce,' says the Lord God of Israel" (Malachi 2:16). Those words were spoken in a time when divorce was relatively easy (at least on the man's part) but that didn't make God tone down His language.
But why did He make such a strong statement? One reason, I'm convinced, is because God knows the problems that divorce almost always causes and He loves us too much to want us to go through them. Divorce always has consequences, and they are almost always painful as you have discovered.
Divorce isn't the end, however, nor is it the unforgivable sin. Seek God's forgiveness for ways you may have failed and then put your life into Christ's hands and ask Him to help you do what is right in the future. Then make Him the foundation of your home, and ask Him to help you raise your family wisely. In addition, get into a church where Christ is preached and taught; many churches today have special programs to help single mothers.