Hello, Anonymous.
The general rule is that a legal action concerning child support is to filed in the state where the child resides. So, from your question, with the child living with the mother in Illinois, the appropriate state to file would seem to be Illinois.
The amount of child support is set by law at a certain amount of the non-custodial parent's net income. In this case, since there is only one child concerned, the proper amount would be 20% of the father's net income. This way the parties know exactly how much is to be paid every month, and there shouldn't be any back and forth about requesting more money or changing the amount.
Setting the support amount is the easy part. The more difficult thing is figuring out the visitation. Illinois courts generally will approve most visitation schedules that the parties can make work so long as it's not detrimental to the child in some way. If the situation is contentious, which it seems to be, you might want to consider hiring a lawyer to deal with that part.
One other thing to note from your question is that child visitation is not supposed to be conditional on availability of the child. Child support is not a payment to see the child; visitation cannot be withheld for non-payment of support. If the mother is indeed withholding the visitation because of non-payment, the Judge will be rather upset about it.
I hope this helps.
Answered on Jun 17th, 2015 at 12:16 PM