It really depends on the parks you plan to visit and you need to do research on the individual park websites. Each one is different.
First, it would be best if you have a toad behind your motorhome and don't plan to drive around the parks with a 40' motorhome. Driving the roads to get to the campgrounds should be no problem if the campground states it will fit your size RV but don't try to do your siteseeing with your motorhome.
As for getting into the campgrounds of the national parks, we have gotten our 40' motorhome in the majority of the western national parks including Yellowstone, Glacier, Grand Teton, Rocky Mountain, Zion, Bryce, Grand Canyon and others. We would not try for Yosemite, although we stayed nearby. We also use national forest campgrounds, state parks, county and city parks and Corps of Engineer parks. We love boondocking, too. Public parks are always our first choice and highly recommend you stay in them for the best overall experience, if you can.
So, yes, you can get into the parks. But....we do this mainly in the western states which are all together different than in the eastern ones. So make your decision depending where you plan to go. Your family are really big and tall. You'll be doing some creative sleeping...perhaps bring along a tent. :) Good luck!
