If your separation agreement does not have any mileage or location restrictions for a relocation, and especially if the father is willing to sign an amendment to the separation agreement that would include a new custody/visitation schedule with you living out of state, then you would be fine to move outside of NC without any court involvement.
If he is agreeing that you move out of state with the children and he voluntarily and on his own free will signs an amendment to the separation agreement with a new out of state custody/visitation schedule, then he cannot force you to move back to NC.
If your separation agreement does not allow for an out of state relocation and/or the father will not sign an amendment (must be notarized by both parties), then you would need to file for custody in court to ensure that you can move outside of the State of NC without the possibility of him filing for an emergency ex-parte custody order.
Attorney with Rosen Law Firm Cary • Chapel Hill • Durham • Raleigh • Wake Forest
Rosen Online | Unlimited confidential access to a North Carolina attorney for $199/mo - click here
The response posted above is based upon the limited factual information made available and is not intended as a full and complete response to the question. The only reliable manner to obtain complete and adequate legal advice is to consult with an attorney, fully explain your situation, and allow the attorney sufficient opportunity to research the applicable law and facts required to render an accurate opinion. The basic information provided above is intended as a public service only, a full discussion with an attorney should be undertaken before taking any action. The information posted on this forum is available for public viewing and is not intended to create an attorney client relationship with any individual. These answers are provided for informational purposes only, a person should consult with their own individual legal counsel before taking any action that could affect their legal rights or obligations.