Agree with Osseous. if you'r comfortable with Class II, don't go to the Arkansas River at these flows - it's highly technical at those flows and you need to be able to row, maneuver, and react without having to about stop and think about what you're doing.
If you've never run Brown's you may want to go down it in a paddle boat or as a rider first to get an idea of what you'll be getting into. Taking the family down on your first time while stepping your game up to a new level may be a bit much.
Pumphouse to State Bridge will be an option, and likely crowded on a weekend, and there's another 50 miles of Class II w/ occasional Class III Colorado River below SB, and more between the Grizzley Creek rest area in Glenwood Canyon and Newcastle. Due to the road construction in Glenwood, an option would be to put in at Two Rivers Park and float to Newcastle.
If you run mainly Class II, you may want to consider renting inflatable kayaks for the teens - sitting on your cat may be boring for them.
Have a great time!
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse