If yaw is controlled solely with rudder toward the live engine you tend to generate a strong roll in the same direction due to sideslip and dihedral effects this is countered with deflection of the yoke toward the dead engine. On jets this yoke or stick deflection may trip roll spoiler deployment with significant performance penalties. Even conventional ailerons deflected against a significant rudder deflection comes at a cost to performance. Adverse aileron yaw just adds to the woes.
If control is the issue as implied by the term Vmca we get back to the rather clinical process of establishing a configuration which preserves good margins of available control deflection to manoeuvre as required while still staying right side up. Up to 5 degrees toward the live engine gives a small lateral component of weight therefore sideslip. This can be used to reduce rudder deflection and return the yoke or stick to something nearer neutral. The available range of rudder and aileron deflections are restored toward normal and the frantic battle against spoilers and adverse yaw stops.
In short stop the yaw with rudder, bank slightly toward the applied rudder, and slowly replace some applied rudder with a careful return of the roll control somewhere toward centre. If it is about the minimum speed for retaining control we must remember that control power is a function of speed and control deflection. The bank places the controls where we maintain greater available deflection so it is reasonable that once achieved the minimum speed may actually be lower. But only after the failure and initial set-up, or during a staged demonstration from the shallow banked condition.