Rivalries are fun, I'm not certain if the players take them as serious as the fans though.
The Avs and the Wings met a lot of times in the playoffs and usually the team that is more eager to win and does everything it takes will move on. The Claude Lemieux hit on Draper is one example. The Moore incident wasn't pretty and Bertruzzi deserved what he got, it was a bit of a retaliation for the hit on Naslund earlier but way out of proportion.
Unfortunately I don't know any of the details of what happened over the last years, times is limited and as much as I love hockey, I don't have the time to follow it closely.
Gotta be focused to achieve something

.