Original: Vyvyan accepts Mike's role as the house leader whereas Mike needs Vyvyan's physique and willingness to act forcibly to enforce his own authority (as was literally shown in "Oil" when Vyvyan became 'Col. Vyvyan', the right-hand-man to Mike's 'El Presidente').
Simplified: Vyvyan accepts Mike's role as the house leader, whereas Mike sometimes uses Vyvyan's muscles and willingness to act forcibly, to enforce his own authority.