Tribal courts are court of general jurisdiction much like State courts, which simply means they probably have the authority to grant a divorce and divide property. The similarities to State courts stop when your talking about splitting a retirement account, 401K, or pension. Before February 2, 2011, this probably wasn't a problem since the courts generally treated tribal court order as "domestic relations orders." This changed becaused the Department of Labor interpreted a Navajo Nation tribal court order as a judgment not made pursuant to State domestic relations law within the meaning of section 206(d)(3)(B)(ii) of ERISA. Under ERISA a domestic relations order, is an an order withing the meaning of section 206(d)(3)(B)(ii) of ERISA, which means made according to State domestic relations law.
The Department of Labor looked to the definition of State udner ERISA in Section 3(10), "[t]he term 'State' includes any State of the United States, the District of Columbia, Puerto Rico, the Virgin Islands, American Samoa, Guam, Wake Island, and the Canal Zone." The Department recognized tribal sovereignty stating that federal law generally does not treat Indian tribes as States, or as agencies or instrumentalities of States. NLRB v, Pueblo of San Juan, 276 F.3d 1186, 1192 (10th Cir. 2002). See also Reich v. Mashantucket Sand & Gravel, 95 F.3d 174, 181 (2nd Cir. 1996) ("[T]ribes are not States under OSHA").
So unless your State has adopted a law to address tribal court jurisdictional issues relating to domestic relations orders, you may have to find a different way to split that 401 K.