If there is no current court order for child support it can be filed for at any time. From the sound of this post, child support was not filed for in exchange for no alimony per an agreement. If there is no court order then I would suggest that the father file with the courts for child support.
The child support calculator on the home site would be able to tell you what the amount of child support would be paid based on both parents incomes and the number of overnights the children stay with each parent along with some other factors. If the parents share joint custody with equal time and make the same amount of money is about the only time that child support is not paid by one parent to the other. I do not believe with the situation described below that the father can get child support for previous dates because of the agreement.
I should also mention that child support and custody/visitation issues are usually looked at as separate issues. One does normally affect the other but they are not usually discussed at the same hearing.
If the parents had a previous agreement for visitations and the mother never enforced the arrangement due to living out of state, the agreement is still valid unless custody has been modified.