I would think they would all recuse themselves and the Chief Justice would then assign a special panel to hear the appeal. Usually, Judges do try to avoid the appearance of impropriety, even if in their heart/mind they know none exists. Per the Texas Code of Judicial Conduct:
Canon 2: Avoiding Impropriety and the Appearance of Impropriety in All of the Judge’s Activities
Judges get to decide this themselves- and no one can force their hand. Our entire system is corrupt as hell.
It's like expecting a 3 year old to police himself in a room full of crystal vases.