Rights of non-resident who lost custody because of "aba

What rights does a parent who fled from her abusive husband have when the childs grandparents (parents of husband) took children back to NC (from OH)and husband was granted full custody because supposedly she abandoned her children…The custody parent has refused and hidden children from her…Not allowing any contact. all Mother wants is ability(right) to call and visit children…

It depends on what type of Court order is in place.
If it is an emergency order you will have a set hearing date to appear and present your case to the judge. These hearings are usually scheduled quickly. Emergency orders are temporary in nature as they are obtained ex parte, which means only one party appears.
If there is a temporary order in place you will have the opportunity to collect and present evidence at a permanent hearing, which is normally scheduled a few months out.
If your husband obtained a permanent custody order, you will need to file a motion to modify custody. To do this you will need to demonstrate that a substantial change in circumstances has occurred which affects the best interests of the children. An example of a substantial change would be your return to North Carolina, and your having a close proximity to the children.
In most cases judges will allow visitation to the non-custodial parent, unless they are a danger to the children. Based on the facts you have presented here I see no reason why you should not be awarded visitation and telephone contact with your children.
I suggest you meet with an attorney in the immediate future to formulate a plan so you may communicate and visit with your children.