This is my situation. I am currently in Russia with our children. My husband gave me a written permission to travel with our sons across the border. However my husband has been unstable over the past year and has been abusive against me in front of the children. I have now decided to remain in Russia where my parents can help me financially and physically to raise our children. I also want to divide our house in New York and my share of the proceeds.
If you do not return to the US, your husband can go to Family Court to seek an order of custody of your boys. The court will first demand your appearance and if you fail to appear, an order will be entered awarding him full custody of the children. However, proof that you are a victim of abuse and competent counsel can help you avoid this result. A good attorney should be able to help you show that you and the children are safer away from the abuser. Much will depend upon what evidence you have in terms of documenting prior abuse and whether you can obtain a custody order from the Russian court before your spouse obtains such order against you in New York. You need help of an experienced Family litigation attorney with practice in international Family Law.