Based on experience with car camping over a number of years and with many people involved, I'd like to suggest you consider that you'll continue to car camp after you get to backpacking, and that you may be best served by having two rigs: the car and the carry.
The best suggestion I've seen above is actually the big, super-affordable Walmart tent. No, it's not ultralight. No, you don't want to carry it in a backpack. However, it's very affordable, very well suited for car camping with a family and absolutely perfect to use for car camping where you want and deserve space, to be able to sit up and to camp in the manner appropriate to such campgrounds. There are other options out there with "front screen rooms" -- excellent! A place to sit in the shade away from bugs, a place to take your shoes on and off, a place for Fido to sleep... Spend $70 and you'll resolve your car camp needs for several years.
Then, you can buy a backpacking tent that's way lighter, purpose built for those trips and that you don't thrash on the car camping weekends. Yes, it will be smaller, harder to get in and out of and unecessary overkill in the car-camps.
Our car-camp tents have been a big Eureka "6 man" (ha ha ha ha, NO) with a screened front room, a Big Agnes Big House 4 and an old mountaineering tent. The big Eureka is the old, steel pole style that makes the Walmart giant domes look so much better and is only a loaner, but I can stand in it and the screened front room is outstanding. The Big Agnes is 11lb, but can be set up by one person, people under 6' tall can stand in it, it's bomber in storms and we added an extra vestibule I can stash bikes and a chair, stove and coffee pot in... With these tents, being able to get in and out without having to crawl as we do with our 2 and 4 person BACKPACKING tents, is huge. Having room for kids and gear is huge. Not worrying about a few extra pounds in exchange for simple comfort is huge. So are the tents. Hey, it's car camping.