Here is the opinion in Garcia v. Gutierrez, from the New Mexico Supreme Court (Garcia v Gutierrez — NM SCT Opinion). An excerpt:

In this case—a divorce and custody dispute between an Indian father and a non-Indian mother whose children are enrolled members of the Pojoaque Pueblo—state and tribal courts have entered conflicting decrees. Regrettably, complete resolution of that conflict lies beyond our reach.

What we can do, however, is conclude that the state court does have jurisdiction. The tribal court—given the importance of the Pueblo’s children to its culture and its future—likely has jurisdiction; and neither is exclusive of the other. As has long been the tradition in New Mexico, the state and tribal courts must share jurisdiction under principles of comity and work out their differences, guided by universally accepted principles of doing what is in the best interests of the children. See Fox v. Doak, 78 N.M. 743, 744, 438 P.2d 153, 154 (1968) (“In making [a child-custody determination, a court’s] controlling influence should be the welfare and best interests of the child.”).

Thanks to T.L.M. for the head’s up.