Where did mom move in the twilight book?

You're likely thinking of the Twilight series by Stephenie Meyer. In the books, Renee Dwyer, Bella Swan's mom, doesn't move to a new place. She remains living in Phoenix, Arizona throughout the series.

While there are some instances where she visits Bella in Forks, Washington, her permanent residence stays in Phoenix.

If you're thinking of a different book or a different character, please provide more context!