Do to your travel distance I would recommend Colorado. Since you suggested staying in motels or like lodging, my first recommendation would be to find accommodations in or near Buena Vista, Colorado. Taylor Park as suggested is also awesome but very crowded. Lake City is also awesome but I have only done the tourist thing there. With boys that young, I figure you have to make it during summer break. I haven't been in that area in near 20 years but recently discuss the quality of the riding with a friend. The area east of BV is first rate for what you want. Many of the OHV trails are dedicated to 50" wide and single track for motorcycles. However there are plenty of miles for jeeps and UTVs.
To start your search go to
www.staythetrail.org/foundation then
www.cohvco.org Once you get through all of that, feel free to ask me anything. If I don't know the truth, I'll make it up :^) Seriously, I'll ask around although I am not well connected in that world. I'd be good for general information.
My favorite place to go is the Red Desert in Wyoming. The Mormon Trail passes right through this area. On a map find Lander, WY. Where I like to go is south of Lander. Look for Atlantic City and South Pass. I think there may be some simple lodging suitable for father and 2 sons. There is a burger joint there also. As I write this, since my Sporting Clays season will be on hold, I may have to head that way myself.
I am going in for shoulder surgery day after tomorrow and my right arm will be useless for a couple months. So with questions, you might have standby for a call.
s/f Steve