N.M. Stat. § 40-9-3
Visitation; modification; restrictions.
A. When the district court grants reasonable visitation privileges to a grandparent
pursuant to the provisions of the Grandparent's Visitation Privileges Act, the court shall
issue any necessary order to enforce the visitation privileges and may modify the
privileges or order upon a showing of good cause by any interested person.
B. Absent a showing of good cause, no grandparent or parent shall file a petition
pursuant to the provisions of the Grandparent's Visitation Privileges Act more often than
once a year.
C. When an action for enforcement of a court order allowing visitation privileges is
brought pursuant to the Grandparent's Visitation Privileges Act by a grandparent, the
court may award court costs and reasonable attorneys' fees to the prevailing party when
a court order is violated.