You cannot file for custody until you establish residency in another state -- normally 6 months to a year. Before that time has elapsed dad can go to court in NY and file for divorce and an immediate return of the children. The judge would most likely grant it and you would be forced to return the children or a warrant would be issued and you would be arrested. You would also most likely lose custody.
let me guess -- you have NEVER filed for a restraining order nor have you ever filed a complaint with the police regarding his abuse.
Parents should remember 3 things: Love your kids more than you hate your ex; when you have children the relationship with the other parent is until death; your children determine what type of nursing home you end up in.
Nothing stated by me should be taken as giving you legal advice or forming an attorney/client relationship.
Attorney-GAL in Ohio.
I've removed the knife from my back, polished it, and will one day return it -- long after you think I have forgotten.