There's a lot going on in this question. It seems crazy for you to owe that much due to a computer error that they just caught. Were you paying via direct withdrawal from your paycheck? If so, didn't you notice that the amount did not add up to the amount the court ordered you to pay? Either way, they will almost certainly work out a payment plan that is based on your income. They can't withhold more than 50% of your disposable income from your paycheck.
Why would you want to get this moved to a state that you don't live in? It seems from what you've said that it's in your interest to keep the case where it's more accessible to you, and moving it to a different state won't decrease the amount you owe because the amount is based on a court order that the other state will likely enforce.
You really should consult with a good family law attorney about this; many attorneys provide free consultations, and might be able to give you more specific advice about how to handle this. Good luck!