As a typical away fan (I go to Sharks games in full Wings regalia) I can offer this small bit of advise...
if your team wins (not gonna happen) leave early or wait till all the drunks file out and have left. The main exodus is when bad things happen, especially when the away team is the winner. With kids in tow, I suggest waiting it out in the arena for 15 minutes and then make your way to the car.
The other option is to stay close to other families, as you wont be a target with more children.
This is more of a sports event suggestion in general, but during playoffs between blood rivals, it's much more important to keep in mind.
Win or lose, I hope you guys have a great time and enjoy the game without the worry of drunks and such.