If a party requests under a law of this state, other than this chapter, a modification of an award confirmed under Section 81-15-115 or judgment on the award based on a fact occurring after confirmation:
(1) the parties shall proceed under the dispute-resolution method specified in the award or judgment; or
(2) if the award or judgment does not specify a dispute-resolution method, the parties may:
(a) agree to arbitrate the modification before the original arbitrator or another arbitrator; or
(b) absent an agreement under Subsection (2)(a), proceed under a law of this state, other than this chapter, governing modification of a judgment in a family law proceeding.