It's more about the players being leaders than the coaches enforcing rules. The HC doesn't need to be a dictator if you have veteran guys that are trying to keep the team together. The Eagles traded for DeMeco Ryans, partially because he's a team-leader. Between him, Jason Avant and even Vick, they did a pretty good job of keeping everyone together.
It sounds like your GM just went off hiring mercenaries and didn't really care about their leadership qualities. You're always going to have some bad apples (DeSean Jackson isn't really a team-first guy), but it's up to the veteran players to call people out on it and stand up for their teammates. Now, the situation with the assistant coach condoning it in is just ridiculous. The Eagles had a similar situation with Jim Washburn, their DL coach, where he played favorites with Jason Babin and busted Juan Castillo's (DC) balls, even though he was an assistant. Apparently he'd call the DC "Juanita." Needless to say, Andy Reid ****-canned him halfway through the season, but it was those 2011 "Dream Team" signings and hires that really sunk the team and prompted the rebuild.
It starts with a HC who knows how to run a football program and hire good coaches. Then you have to decide what players are actually helping your team, or just taking a paycheck.