I'm sorry to hear of your dilemma.
First of all, the mother hasn't been in the state of NY long enough to petition the courts for divorce, support or custody.
Presuming that you were not married in NY, and never lived there as husband and wife, once she has resided in NY for 24 months she can file for divorce, however, because the court does not have personal jurisdiction over the children, the court is unlikely to be willing to rule on custody matters.
That being said, it is definitely against your best interest to allow a divorce to go forward in New York. If the court somehow gains the ability to order custody and support issues, you will find that they are more sever than Texas. For example, child support
in NY continues not jut to age 18, but to age 21 in most circumstances.
I urge you, while you still hold all the cards, to file for divorce in Texas. You will be happy that you did later. If you file in Texas and get her served before she can file and serve you, you will definitely be in the superior bargaining position in both property distribution, custody and support issues.
I wish you and your children the best.
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