Not sure if a different tent will ameliorate all this. However, as you're talking about car camping, Kirk, I wouldn't fool with those lightweight confections offered by backpacking-type tent makers. You're right, Sierra Designs and The North Facealong with Mountain Hardwearall make tents big enough for six or more people. But they're basically two-person tents that have been bulked up a little.
Better just to get a big tent that doesn't care how much it weighs. As you say, the 4Runner is carrying it, not you. One good possibility is the Equinox 6 from Eureka! ($499; www.eurekacamping.com), which can comfortably sleep six in a big single room with near-vertical sidewalls, so there's no sense of crowding. Six feet seven inches at its center, the tent will let you stand to get dressed. It has an aluminum frame and tough fly materials for durability. You'll be packing a hefty 18 pounds 12 ounces for this baby, but I suspect your Toyota won't mind. L.L. Bean also offers a big campground-style tent called the King Pine Dome ($249 in the four-person model; www.llbean.com), which offers a screened front "porch" for comfortable sitting on buggy evenings. While it weighs 25 pounds 15 ounces, it's also much cheaper. Regardless, either of the above would work well, and I'm sure keep the brood from complaining too much.
Interestingly, canvas tents are also making a comeback. They're really heavy, but hard to beat for durability. Campmor sells the Trek canvas tenta whopping 57 pounds!in a seven-person model for $360 (www.campmor.com). It has a polyester fly to shed water and the sun, keeping the tent drier and cooler. Very plush. Note they're out of stock right now but are expecting a new shipment toward the end of May.