What happens when Charm pulls Vex away while Rengar is played in response?

A showdown cannot start while anything is on the chain. Charm is played but does not resolve, then Rengar is played and resolves while still Stunned. Vex's trigger resolves, then Charm resolves and Vex is in base. On cleanup, Vex loses control, the staged combat showdown starts with only Rengar present, and Rengar will conquer if not removed before the showdown closes.