Bragg was kept in command by Davis at the end of the meeting. Bragg did have his enemies within the army, but he also had a lot of supporters(AP Stewart, Wheeler, Bate, Maney, Strahl, Manigault, Deas, Anderson, Walthall, JK Jackson, Stevenson, Wright, Clayton, and others). Bragg only left when he asked to be relieved of the command after the debacle at Chattanooga. As to Longstreet going back to VA, that was because of Lee, Lee wanted Pete back.

Lee