The court can order any money you place into the LLC disgorged. The only way to avoid this outcome is to create your business in an offshore nation that does not cooperate with U.S. authorities (e.g. Nevis, Beleze, etc.), and then create something called a "trust protector," under which if any attempt is made to sue you to disgorge funds, the trust protector steps in and severes your control of the business, so that you cannot comply.
This sort of business structure requires a lot of very sophisticated planning, and only a few U.S. attorneys can set it up for you. If that's something you are interested in, you will need to find an asset protection attorney with experience in offshore business entity formation.
Another alternative would be to try to work out a stipulated agreement whereby the other parent agrees to waive his//her rights to the arrears, in exchange for something like an ownership interest in your business. Then, he/she will know exactly how much you are making and he/she can get a piece of the action for the children's benefit.
Obviously, giving up a measure of ownership is not what you will want to do -- but, you are behind the eightball, because a child support obligation like yours cannot be avoided -- you are stuck with it for the rest of your life, unless you can either pay it in full, or get the other parent to agree to accept a settlement.
Hope this helps.
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