Just some thoughts from a family that has gone cross country before... You will inevitably be camping in rain. Rain and a pop up are NOT a fun mix. You will be pulling into a campground in the rain and have to set up. You will have to break down in the rain and stow a wet pop up camper for a day's drive. You will then have to set up that wet pop up, which will have likely leaked and gotten your mattresses wet. Now you are sleeping in a mildew smelling pop up on a wet mattress.
You will struggle to find campgrounds along the way that have "decent" bathhouses. You will find campgrounds that have non heated showers. You will find that you are far away from the bathhouse at times, because you probably won't be able to set up reservations in too far advance. Middle of the night trips to the bathhouse with young kids can be interesting at best and too late at worst.
As others have said, you will find some areas that may not allow you to stay with a pop up because it doesn't protect against wildlife.
If you are serious about wanting to take this trip, you might be a LOT happier if you bite the bullet and get a hard sided (or hybrid) camper and suffer with lower mileage and higher initial cost. You won't have the concerns about setting up a pop up in the rain, mold and mildew from stowing a wet pop up when you leave, have the option of a bathroom in the RV, be able to cook inside the camper, have a little more security and privacy amongst the other benefits. You will be driving across large stretches of NOTHING in northern Texas. I can tell you from experience (especially with young kids) that it is very nice to have 20 or 30 gallons of fresh water and a bathroom in the trailer. Nature calls even when there aren't any local facilities to make the experience easier and cleaner...
If you decide you like camping, you have a decent trailer to continue camping. If you decide you are one and done, you can sell the trailer within the year for roughly the same money you paid for it. The difference in mileage between a pop up and a travel trailer is likely to be 4 or 5 mpg's. That is a lot of gas, especially for a 5 or 6,000 mile round trip.
You have to decide if money (better mileage with a pop up) or convenience and comfort (hard sided trailer with kitchen and bathroom) is more important. If you were just doing weekend trips and could cancel if weather was bad, it would be an easy decision. I've been on that trip before (Maryland, through the south to California, up the coast, back across the northern part of the states and back home in 6 weeks), and I would take the upgraded creature comforts of a hard sided trailer with a bathroom, air conditioner, more privacy and less concerns about the weather.
Either way, it has the potential to be a fantastic trip when all is said and done.
