You are in a bind. You need, and I can't stress this enough, YOU NEED a family law attorney. If DCFS is involved, you need a lawyer YESTERDAY. Don't talk to DCFS without an attorney, they are not your friend. Don't sign any DCFS forms without an attorney present, NO MATTER WHAT THEY CLAIM THE FORMS ARE FOR.
Bottom-line, if you're serious about keeping your children, get a lawyer. Don't go cheap here, you will get burned.
I agree with attorney Gotzh. You need an attorney! It seems there are three things that are getting confused with each other. One is child custody and child support, the second is whatever is causing the state to threaten to take your children, and the third is your proposed solution of giving custody to your daughter. All of these are separate issues and very important. You should go to an attorney who represents you and ask for their advice, then do what they say. Do not try to resolve this yourself or come up with solutions on your own such as giving custody to another person. I would add that if you cannot afford an attorney you might possibly qualify for free legal assistance if you meet criteria according to federal poverty guidelines. Since you live in Illinois, I'm putting a link to the Illinois legal aid web site below.
Far too many variables exist in the short post you wrote for any further observation by me. Many attorneys have information posted here on Avvo.
You might find my Legal Guide helpful "How to Choose A Lawyer For You"
You might find my Legal Guide helpful " What Do I Tell My Lawyer"
No one can know what the record is in the case because online we cannot see your documents. You need a lawyer. Check with a lawyer in your locale to discuss more of the details.
I agree with Mr. Gotzh!
Good luck to you.