My stepdaughters' mom have left the state of Texas( taking the girls) and went to Atlanta, Georgia. She has told my husband she is not coming back, and he will never see them again unless he comes there to visit them. What can we do to get the girls back to Texas where they were born?

Not enough info. Was your husband married to this woman? Is there a custody/visitation order issued by a court? If so, where was it issued? How old are the children? How long ago did they move?

Bottom line here is if there is a custody/visitation order issued by a court and her move to GA violates that order or prevents your husband from exercising his visitation then he goes back to court and ask that she be cited for contempt of court and that he be awarded primary custody. If there is no order, then he needs to move fast to file for custody in TX before the children establish residence in GA. I would highly advise he hire a Family Law attorney as this appears that it will be messy.

... he needs to move fast to file for custody in TX before the children establish residence in GA. ...

Actually before Georgia becomes the child's "home state", as defined by the Uniform Child Custody Jurisdiction and Enforcement Act. The period the child has to be there for establishing Georgia as the home state is six months.

Thanks for your help. If they are gone for 6months and they establish residency, is it impossible to get them back? Is it legal, when there is no court order? We have a written agreement that has been notarized, will that stand up in court when seeking custody.

Once you file that should stop the clock on their obtaining residency. But if there was no court order, its going to be a tough sell, Get an attorney now!