Your boys might not want to travel with you all the time, but my 20 year old just came with us on our spring break trip, and is planning to come with for our two week trip this summer. Our 28 year old has tagged along with his wife and daughter when we've gone on weekend trips, and his wife and daughter came with on our Yellowstone trip last year.
I'm glad we've always had the room for friends and grandkids to join us.
Length isn't as big of an issue as some make it out to be. I agree that the 28' or less is probably best for your F150, and there are lots of floorplans in that size where you can have room for six or seven.
We've got a 2016 F150 with the tow package, and currently pull a 30' trailer. The length is at the edge of the envelope for what most people would be comfortable with, and if you don't have the right hitch or experience, it might not be right for you. I've been towing for about 20 years, and don't fear it. Neither does my wife, who has her CDL and also some experience driving large vehicles.
We've traveled with a 30' motorhome pulling a dolly and a van, and also with a 30' fifth wheel, and never had a problem at Big Bend, Guadalupe Mountain, Grand Canyon, Zion, Yellowstone, Grand Teton, or any other park out west.
You will be limited at some NFS campgrounds, but even there, the length of the site is often listed as where the wheels can fit.
On my 30' Grand Design, I've got 10' of overhang behind the rear axle. As long as there isn't a tree in the way at the back, we usually fit into sites listed as a 25' foot max.