I think you actually had a good idea to start with, to include RMNP. But you should include it only as a single "take a break from the mad rush" day. Reserve a campsite at Boyd Lake SP, spend the night. In the morning unhook, pack a picnic lunch, and drive into RMNP. Drive up the old Fall River Road if you're brave, and return eastward on Trail Ridge Road. Look at a map of the park beforehand and decide if there's a short trail or two you'd like to explore during this time. Take it at a leisurely pace. When you get back to your campsite you can take a swim or hang out by the lake, grill a nice dinner, have a campfire if you like. Then you'll be recharged for another big day of driving.
Personally I prefer the Tetons to YNP. Many feel the opposite. But to me the Tetons represent "the West," a feeling of wide open spaces with a great mountain view and the reflection of those mountains in the water. YNP feels more crowded and bustling with traffic, which I prefer to escape, and I felt like one day of bubbling mud and geysers was enough for me. YNP lacks the view of mountain peaks that I like. So to each his own, but try to think about what excites you. YNP does have some nice waterfalls and a ton of wildlife.
I wanted to go back to Tetons last summer but didn't make it. This coming July is looking pretty good for it, though. I hope to take that boat ride across Jenny Lake and hike a bit up the west side. Pedal my bike on the multipurpose trail south of the lake. Paddle my inflatable kayak around String Lake or Lower Slide Lake. Maybe ride through the white water farther south. Take a soak in Kelly Warm Spring. Hike to Paintbrush Canyon. Shoot lots of pictures. I may stay a couple nights in one of the established CGs, but most of the time I intend to boondock on nearby NF land. I would also like to drive the Bear Tooth Hwy, on the NE side of YNP, so I guess I will get to see some of that park too... just passin' through.
