“As a general rule, an arbitration clause is only binding on the parties to the underlying agreement and not on third parties.” Edward Family L.P. v. Brown, 140 P.3d 525, 530 (N.M. Ct. App. 2006). However, the New Mexico Court of Appeals has recognized the existence of an exception “based on principles of equitable estoppel”:
The denial of a motion to vacate is also reviewed for abuse of discretion. Edward Family Ltd. Partnership v. Brown, 2006-NMCA-083, ¶ 17, 140 N.M. 104, 140 P.3d 525. An abuse of discretion occurs through application of the incorrect standard or substantive law, reliance on clearly erroneous fact finding, or application of correct legal standards in an incorrect manner.