Is there any financial assistance for a mother wanting to get custody of her children? She is currently separated and barely able to support her children. She left him because of 20 years of mental and physical abuse with both her and the children. Husband is threatening to take her to court to get custody of youngest child who is 9. They both live in North Carolina. She is wanting to move back home, which is out of state, where she can have support from family and friends. Can she cross state lines with children if he is abusive and she is taking them away from that abuse?

By "financial assistance" do you mean assistance with attorney fees? I doubt it. Has she checked with any legal aid offices in her area?

Yes, absent a court order to the contrary, she is allowed to take the children with her if she decides to move out-of-state. In other words I can find not a "parental kidnapping" statute, which would prohibit either parent from removing the children, in NC's criminal laws:

"...
Article 10 - Kidnapping and Abduction.
§ 14-39. Kidnapping.
§ 14-40. Enticing minors out of the State for the purpose of employment.
§ 14-41. Abduction of children.
..." North Carolina General Assembly - General Statutes - Chapter 14: Criminal Law.

However she should be aware that whether she does take them out of the state, their father can sue her for custody, and for six months after the move exclusive jurisdiction would be in N.C.

Parental kidnapping only comes into play when one parents hides the children from the other. But, as noted, he could file in NC and NC would have jurisdiction. And she could be forced to return the children to NC.

It would be better if she can file in court for an emergency order to move. She should check for women's support groups in her area.