But first, I'm not exactly sure what you mean by tents with "inflatable bottoms." Bouncy castles for fun in the backcountry? Really, inflatable sleeping pads are a much more obvious and less fallible option in this category. If one gets dinged, you've still got five others to fight over.
There is the AirZone Condor ($599; www.airzonerecreation.com), however, which has inflatable "ribs" that replace the poles. It'll hold six, so it's a big tent. Its 29-pound weight is on the high end, but not unrealistic for rafting or paddling excursions. So that's one choice.
Otherwise, I'd stick with traditional tents. Eureka!'s six-person Equinox ($320; www.eurekatent.com) is a tried-and-true performer that will house your brood; nice, upright design, aluminum poles, good wind and weather resistance. It's almost 19 pounds. The six-foot-seven-inch-high Equinox isn't ideal for super-windy conditions, but works just fine for general three-season use. And it's a great value—check Campmor.com for deals to make it an even better buy.
Interestingly, Sierra Designs' new Bedouin 6 is just as competitive, price-wise, at $300 (www.sierradesigns.com). It also sleeps six, and has vertical clearance of just over six feet so you won't feel crowded. Weight is a little more spartan than the Eureka! model at just over 17 pounds. The fly offers fuller coverage, too, so that's one advantage in its favor.
Lastly, Kelty's Pagoda 6 ($400; www.kelty.com) offers a low-profile design that would be your most weatherproof option, while still sleeping six. It weighs 20 pounds, but that's still just over three pounds per person, so not bad—and fine for paddling. It also has a large vestibule for storing wet shoes and dogs, which might be handy.
Read "Who's Your Daddy?" from Outside's April 2004 issue for a cautionary tale from the frontiers of father-son bonding.