My experience has been that the months of June thru August are the busiest in YNP. Why? Weather, and school is out. The altitude (8,000 ft), and June - August are the only months that they don't get at least some snow. The Grand Loop is 140 SLOW miles long. Since you have kids, there's nothing you can do about the above. Add that YNP was established before the Model T was invented, so the CGs inside the park were designed to protect the parks flora and fauna. Your rig won't fit in many of the CG spots, and the larger ones may be booked solid all summer, IF they take reservations at all.
I stay at Grizzly RV Park just outside the West Gate and I pass thru the gate early each morning before the new arrivals get there and have to buy their passes. Granted that the the West entrance is 15 slow miles from the grand loop, but you aren't in a tunnel. There are are many sights and animals to see on the way to the Loop each day.
I try to do a quarter of the Grand Loop each day. It doesn't matter if you don't get to see everything. You'll be back. I've visited several times, starting with my parents when I was about 8 years old and I'm rubbing up against 70 now. Its amazing that my normal high blood pressure seems to just go away when I'm there.
Wonder if I could deduct the trip as a medical expense? :)
