I have a good idea.
How about for one tournament, Kai and Wyatt pretend that there is no bad blood between them. They don't have to seek out conversation with each other, but just not respond to what the other says with rude comments and not have any preset animosity at all. Then, possibly, they'll see that neither of them is a bad person and learn not to hate each other. For every tournament this works at, they should try again until things settle down.
Sounds pretty fair, no? Not asking you two to be friends, but I don't like seeing two good friends of mine argue with each other and throw jerky comments around, whether it be to the other's face or behind their back. You both have your flaws and disagreements, but I don't doubt that you'll be able to tolerate each other.