Maybe RED HOT can mention to her brother that a potential coach is somewhere in the town, enough to make the group look for the coach the following day.

In the next day Vance's character will place the Quatre strap at the lost and found, luring the coach in disguise. When her identity is discovered she will relent and agree to a Gunpla battle against everyone to see if they're worth her time to coach and let them register for the tournament.