There are many ways you can make your adventure fun and comfortable, but you will never know until you go out and try.
We also travel as a family of 5 and pull a little solid side pop up trailer. My wife can set it up by herself in under 30 seconds, my best time was under 10 seconds. It's insulated, has heat, AC, water tank and has enough room for all 5 of us. It's also overbuilt for it's size. I did do a axle flip and 31x10" tires for off road use.
BLM land around Capitol Reef
Random beach at an end of a dead end trail at Lake Mead.
Ski and snowboard base camp in Mammoth. As well as "camping" at the hot springs after a day of skiing.
Truck not hooked up but enjoying the view on the Homer Spit in Alaska.
We love this little thing, it tows easy, we store all camping essentials in plastic bins that either stack in the back of the Suburban or tuck under the beds in the camper. Best of all once we get into an area, we can set up base camp, unhook the trailer and go explore trails in the truck without the added weight of gear.
We considered an RTT, while it would be an absolute dream for the kids, I spent twice as much on the trailer and fully protected from all the elements and always have a dry comfy bed even in a wind, thunder or snowstorms where an RTT would be impossible to setup.
Ultimately, start by actually getting out there. Use what you have or get a tent at walmart and start with that. Figure out what worked what didn't, make adjustments and go out and try again. And to answer one of your questions, YES, there are many families traveling and exploring in your TRD, it's a great and capable truck even without 4wd with plenty of room in the bed for all your gear.