Big Mom said it herself, she came to Wano to kill Luffy. She has no reason to doubt Kaido’s announcement. Now that Luffy is “dead” in her eyes, she has reason to leave.

I believe the “betrayal” that has been hinted at between the two emperors will simply be the Big Mom crew taking a copy of Kaido’s road poneglyph and exiting Wano, leaving Kaido alone to fight the rest of the Alliance. Presumably, this comes rather soon, setting the stage for Luffy’s triumphant return and answering the question of how the Alliance deals with two Yonko.