What to Do If You're A Supreme Court Justice and You Think Your Court's Own Rule is Unconstitutional

In the view of Justices Corrigan and Young, you don't follow the rule.  The rule is MCR 2.003, which says that the Court can decide whether a Justice should be disqualified from participating in deciding a case. Here's the order in which they explain why they're not participating in the disqualification process described in the rule (the rule is unconstitutional), and Chief Justice Kelly and Justice Hathaway explain why they disagree (Justices have a duty to participate until the rule is declared unconstitutional).  To refresh your memory, the order is the promised coda to the order of January 28 in which Chief Justice Kelly, and Justices Cavanagh, Weaver, Markman, and Hathaway denied Geoffrey Fieger's motion to disqualify Justices Corrigan, Young, and Markman. 

The case at issue is Pellegrino v. AMPCO Parking (majority opinion) (concurring/dissenting opinion).

The Michigan Lawyer has a good post gathering the facts and documents, and this MIchigan Lawyers Weekly story supplies the background: “Court rule, case law in conflict: MSC to determine if trial judge tipped the scale, based on race.”