This has become one of the biggest problems in the area of family law. The first thing you need to know is whether the country she is in is a member of the Hauge Convention and if the country is a member, does the current political circumstances of that country enforce the terms of the Hauge Convention. You are unfortunately in for a long battle. Hire a good lawyer and be prepared to spend some time and financial resources in your pursuit. Best of luck.
You need to consider several factors prior to engaging in a modification. First, consider what the other side may say about you during the modification. Everything that has occurred since the last order is "in play." Be prepared to answer any questionable activities on your part. Many times, in Bexar County, the Judge will order a drug test at the court house. Your attorney should make that request at the temporary orders hearing. Please note that they may request that you do the same....
You have to follow the orders of the court. She must do the same and if she does not, you can seek attorney's fees for the filing of a contempt action. In the event the court finds her in contempt, attorney's fees are mandatory. If she has money a lawyer may take your case for a lower fee due to the fact that they can recover from the mother.
Orders remain in affect until they are superseded by a new order. Note, there is typically language in a new order that says any provision not specifically modified by this order shall remain in full force a affect.
If you paid what was ordered, you are in compliance with the court and there is no underpayment. She would have to file in order to receive an increase. Hire a lawyer now and pursue obtaining custody. I would want to know what the age of your children. It appears, given the amount of years you have been paying, that they are over the age of 12. If that is the case, the procedure to obtain custody should be fairly simple. Please note, that "simple" is a relative term.
Considering there has been violence, you may want to discuss with the lawyer you retain the possibility of obtaining a protective order. The difference between a temporary restraining order and a protective order is the ability for the police to jail a person who violates the protective order.
If he agreed to pay 330 a month in child support in the decree, but has not been paying though the attorney general, he will have to prove that he has paid that amount each month. In addition, he would have to show a "material and substantial change" in his earnings to lower his child support. For one child he must pay 20% of his net available resources and 5% more per child. I would recommend that you retain a lawyer and pursue a modification in child support. Be warned that he may...
I think you need to hire a lawyer as soon as possible. Each modification case is different. The first thing a lawyer needs to do is review the order you are seeking to modify. Your description regarding the possession and the interactions would lead me to believe that you clearly have a basis for bringing a suit to modify.
If there are no orders prohibiting you from taking your children out of town then you should have no concern. I would agree that if your husband is that crafty and finds a lawyer to move that fast, there could possibly be a mess waiting when you come home. Obviously you are thinking about a divorce or you would not have asked this question. I would contact a lawyer and get some guidance that is particular to your situation.
If the court lacked jurisdiction, there is case law out there that says any order is void and that can be collaterally attacked at any time. That said, the order is probably going to be entered even over your objection. I think that a mandamus might be the more appropriate plea to the court of appeals, but that would take research to determine. Please retain counsel.