I very much doubt that the courts would have the authority to make you show you books to them. They will probably ask for wage records or an itemized statement as to his wages. Make sure you have everything straight as to the ownership of the company. They can do nothing to you. If you had a successful business and he did nothing but watch daytime TV, they could still do nothing to you about your business earnings.
Don't give in and let them look at your books. If they request it in discovery, your husband's attorney needs to object and not give them the info.
A lot of what is going to happen depends on the original order. If there is no school tuition mentioned in the original divorce, chances are they will never require him to pay it now. In order to get these things changed, she would have to show a substantial change in circumstances that could not have been anticipated at the time of the divorce. For example, to go in and try to raise the child support amount because the kids are older. That is not something that was not anticipated. But, if someone's wages substantially change, then she can go to court for it.
In Illinois, courts can order educational support regardless of the age of the offspring. Support applications can be filed before or after the person reaches the age of majority, and orders can apply to expenses related college education or other professional training after high school. By law, expenses include room and board, academic fees, tuition, transportation, books, application costs, medical expenses (including insurance), and living expenses during the school year and recesses. Judges must consider the financial resources of the parents and child, as well as the standard of living the child would have enjoyed had the parents not divorced (750 Ill. Comp. State. 5/513).
The $3100 can only be collected if it was something that was ordered previously but not paid. In other words, if he fell behind in his payments. If it is just something that she wants that was never ordered before, he will not have to pay.
I am only assuming some of this, since I don't have the original court order here. But, as a general rule, you can collect what was ordered by the divorce but not paid, but you can't collect a back amount that was never ordered anyway.
Let me get a little more information.
Was he making a comparable income at the time of the divorce?
Does the divorce say 1/2 the tuition, no matter what the cost?
Does he have joint custody?
Is she trying to modify the divorce (is that the action she filed recently)?
I am so sorry, I must have missed your further questions. You are certainly right about that wording being "vague" about the school costs. It is complicated by him not having joint custody since that may have given him more "say so" about the schools they go to, and the extra curricular activities that may cost him money.
Part of the problem with that high tuition is that if he has been paying it before, even it has been a huge financial burden, the courts will likely not want the children to have to stop going to those private schools. It will be up to your husband to prove that she should be responsible because of the money she makes and because it is her choice to send them to a particular school.
He should set a certain amount that he is able to pay towards their schooling and compose a financial statement showing how much he has for bills, regular child support, and things like that. It can clearly show how he has no more disposable income to pay expensive schools.
There is no clear laws or cases for each circumstance and unfortunately this case is one that will have to be decided individually.
It should be obvious that she makes the decisions, makes much more money, and should pay the bulk of the school costs, unless they are move reasonable.
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