There is no red button as such (at least as far as Airbus is concerned). The computer decides that something has gone wrong and invokes an alternative law. You'd have to start pulling circuit breakers to manually trigger a reversion.

> Commercial airliners are stable when flying.

This is not necessarily true. All modern airliners have aggressively swept wings. This generally makes them susceptible to dutch roll in some phases of flight. They are fitted with yaw dampers to control this tendency.