At the end of GF III, I think Al Neri is second-in-command to Vincent, but I think Michael and Connie are both functioning as consiglieres/ Dons Emeritus to Vincent. Connie even "makes her bones" by killing Don Altobello.

I think it's fair to assume that whatever structure the family has after GF III, Michael and Connie are both going to be part of it.

The earlier scene, after the attempted hit on Mike, is Mike reasserting his control. He doesn't want Vincent, Neri or Connie to think he is old and helpless. At that point I don't think he believes Vincent is ready for that kind of authority.