Gen. Meade did not agree with Gen. Grant's conduct of his battles either but that did not keep Meade from working with Grant as his commander. Longstreet arrives under Bragg command on Sept 19th. and almost immediately takes sides in the conflict and trys to assert himself. Longstreet may have been to use to the relationship and latitude he had with Gen. Lee, but he failed to act professionally in a military manner which could have stabalized the command situation between Bragg and his other subordinate corp and divisional commanders.
I am sure that Bragg was somewhat intimidated by the reputation of the "great" Longstreet coming west to be a part of Braggs army. I would think that Bragg would have been a littled worried that Longstreet was coming west to relieve Bragg of his command. Longstreet should have realized this, but Longstreet seemed to have his eyes fixed on exactly that prize. I wonder IF longstreet had in fact been supportive of Gen Bragg instead of becoming an adversary that they may have been more successful in the capture of Rosecrain's Army and Chattanooga? Could Longstreet have changed the entire course of the war?