Hi A.,
We did this over the summer to pay my sister-in-law to watch my son. She watched him in our home for 3 months. They pay by the day and she received 10 dollars per day. We also had a copay which was determined by the state. As previous people responded there is a difference in pay when it is outside the home but I do not think it's much different. It will be more if you are liscensed.
I think it's great that you want to help this mom out. I was lucky enough to have family; I don't know what I would have done without her help. It's so hard to find affordable quality childcare in the city.
Here is the link to DHS and all the info you should need. The Co-Payment Fee Scale and the Child Care Payment Rates are all listed. You can also download the application form for the mom to fill out and send in.
http://www.dhs.state.il.us/ts/ChildCareDevelopment/CCD/
There is alot of paper work before you get paid so be sure you get started early. Hope this helps.
~L.~