I agree Vaughan could have stayed on, however PC made the decision based on his greater knowledge of the player than we have. Personally I think it was the right decision as given the way the game went and the challenges that were going in I think Vaughan could also have lost his cool and joined Naismith in the dressing room.
Byrne was temporarily switched to cover for Naismith until a better solution could be found, he moved back to the right pretty soon after the substitutions and switched to three at the back with Burn on the left and James on the right.
The hoofball you complain about was due to the pressure being exerted by Derby as they searched for a second goal to kill off the game and was a response to the fact we had just had our game plan destroyed. It was a response to get us to half time still in the game and give PC the opportunity to get us in the dressing room and rearrange the system. Which he did very successfully.
The awful showing in the first half, as you call it, was a direct consequence of the sending off and I applaud the players for their response and for staying in the game. Until we were able to reposition ourselves it was always going to happen that Derby would throw everything at us. We pinned Derby back in the second half and caused them a lot of problems whilst they were unable to penetrate our defence.