Re: Yellowstone - the park is much bigger than first timers typically imagine it will be and the loop roads have low speed limits. They tend to be very slow and trafficky during prime summer season, some parts of them more than others especially if a buffalo, moose, or a bear happens to be standing somewhere within sight of passing traffic. With the appearance of any significant wildlife people tend to get very excited, sometimes abandoning their vehicles in the middle of the single lane (each way) road and running into the field with cameras. Sometimes there are one or more buffalo (or dozens) standing in the roadway and they don't go anywhere until they're ready. In other words, expect delays.
Yellowstone is also not really on the way to anything in the sense of just jumping off an interstate, seeing it, and jumping back on. You pretty much have to be intending to go there, and there will be several hours of two lane hilly twisties just getting into the park and out of it from any direction, in your case, most likely from the north on US 191 or 89, and to the east on US 14>20>16.
IMO, it would be a bit of a waste to go there just to drive around the loops and not get out and see and experience some of the sites (meaning more crowds and wait times), but even if all you did was drive a slow parade lap around the loops that's a pretty significant diversion from I-90. Typically Yellowstone (and Teton, which in some ways I like more than YS) would be a several day trip by itself. My family and I enjoyed the parks themselves (Yellowstone and Teton) but we also enjoyed interspersing park-heavy days with evenings walking around West Yellowstone, seeing the shops, having pizza, etc. One of the things we still talk about was one 4th of July having a snowball battle in the park that afternoon (yes, there were/are still snow drifts in higher altitude shady spots in YS park on the 4th of July) then watching the fireworks in West Yellowstone that night, some of us wrapped in blankets against the see-your-breath chill.
Also, if you're planning on going east out of YS to pick up I-90 to the Devil's Tower - Rushmore area, be advised that it's a twisty up-and-down two lane coming out of the mountains from YS into central Wyoming, with a LOT of deer, elk, and even the occasional moose on and near the roadway. We did that route in the summer of '14 (US 14 > US 20 > US 16 between YS and I-90 in Buffalo, WY) and had several close calls with deer to the point that I got semi-paranoid going around blind curves. At one point we came around a curve and surprised a doe and a fawn standing in the roadway. The doe ran down the right side bank in a panic but the fawn ran the opposite way and got trapped against the vertical bank on the left side of the roadway. We came to a stop as the fawn ran around in the roadway in a panic trying to find mama and the way out, so I used our vehicle to slowly herd the fawn away from the vertical bank on the left and toward the drop off on the right that mama had run down. You're not finally clear of the hilly twisties until you come up and over the range of hills in the Bighorn National Forest and descend into Buffalo, WY. I was glad to reach I-90 that evening, but then at dusk we had another close call with three deer on I-90 between Buffalo and Gillette.
In other words, count on that route taking longer and being more demanding than you think.