IF the papers did not specify any particular amount was to be paid but that the party had agreed between themselves for any amount on a weekly basis then the court does not have the authority to say "We decided you have to go back and pay at least minimum wage child support for the last 10 years. A judge decreed no child support was ordered and the 2 parties agreed. She can't go back and change her mind now.
Minimum wage child support in Oklahoma is about $168 per month. If he did pay anything to her and it wasn't even that much she still can't make him pay any back child support because he was never ordered to pay it. Therefore he did not owe it. There is no bill because he wasn't ordered to pay. All he needs to do is have a copy of his order and any proof he has he paid anything and he is clear.
Also, going back to school for free has nothing to do with going after child support. More income would mean she'd have less chance of getting financial aid. If she has LESS income she'll have a lot more aid given.
IF she filed for food stamps, medical assistance, or child care then the state filed in her stead or she would not be able to receive that assistance. As sad as it is the state will require she file so she will increase her own income and use less of the states assistance. So they require her to file.
I would also say that if he has been paying her anything over the years he might need to find some sort of way to sit down and think back to what he paid her so he can have a list that shows he paid her something. Even if he didn't pay anything.
If the state filed the paperwork for child support she may not even be in court. She may not even be aware of the court date. The state has the father's income tax returns now and they know what he's claiming he has earned. They will base his new child support on his current income. If he had a huge income and it's recently gone down drastically they may ask what happened and order a lower payment but that's not likely if he just quit a high paying job to take it easy or semi retire.