Larry N. said:
If you drive six hours every day, you're not going to have any sightseeing time to speak of. Driving 6 to 7 hours for each day you drive is one thing, but if every day is a driving day, everyone will be tired, no one will enjoy it, and you won't see much except passing scenery. There should be several days with no driving planned, other than within the park itself, or the local sights.
That 50 mph average people are talking about generally includes meal time, rest stops, and fuel stops, all of which bring down your average for the day, even though you might be traveling 65 mph, or so (don't plan on higher speed -- the RV won't like it). So if you figure about 2,000 miles one way, at 50 mph, you'll have 40 hours, or a workweek's worth, of driving time one way. Obviously you'll have the same going back. That's 5 8-hour days each way. And you have two weeks? So you've maybe got 4 days to spend looking around if you drive that 8 hours each day going and coming.
It's doable, but you'll be tired when you get there and tired-er when you get home. You can have fun, but you need to be aware of what this really entails. You also need to keep in mind that once you're off the Interstates, especially in Wyoming, you'll likely average closer to 35 or 40 mph, perhaps less. Some of those roads slow you down more than you might think from looking at a map.
OK, there have been a lot of "discouraging words" here, so I'll add something not quite so glum. Though you can't see all of Yellowstone in four days (if that's how it actually works out for you), you can see quite a bit of stuff (there's a LO-O-O-TT to see), and it'll be a different kind of experience than anything you can get in the east, lots to see, lots to learn, lots of pictures/videos to take, etc.
Be sure you get on the Yellowstone website and heed their cautions. It's bear country, but a little care makes it not a problem. It's dry air, for the most part, and dehydration can catch you unawares, but drinking lots of water should take care of that. It gets chilly at night, 40s, maybe occasional 30s, even in the summer, at night, with bright, searing sun during the day, even if it's only 60-70 degrees out for a high temp. Bring jackets. You're at 6,500-8,500 feet, depending on where you are in the park. Bring sunscreen. Wear hats and sunglasses.
Even with all the above you can have a good time after you get there, but just be aware of what you are getting into, including the short visit.
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