She can move out whenever she wants, as could you. There may be legal implications, but as far as custody both of you would have 100% custodial rights to the children absent a custody agreement or court order.
If she decided to move in with someone else, you could file a lawsuit, show that this situation is detrimental to the children and that they need to be home with you instead of with some unknown person.
Ketan P. Soni
The Rosen Law Firm
4101 Lake Boone Trail, Suite 200
Raleigh, North Carolina 27607
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 but a full discussion with an attorney should be undertaken before taking any action.