It's been a very long time since I drove 287, and long before I even thought about an RV, so...
First, we've had a LOT of rain up here. You definitely want to check with CO DOT to make sure the roads aren't flooded! Also, we made a trip to Yellowstone 1.5 years ago (again, pre-RV) at another high-water mark. 287 wasn't even an option then. The good news is that you don't lose too much just taking I-25 to Cheyenne and then I-80 across Wyoming (I wouldn't take I-70, but that's just me.) If you haven't driven I-80, a word of warning: gas up every chance you get! Also, watch for high wind warnings. We took 189 out of Rock Springs, but we were going to Grand Teton first. It gets a little narrow in places (and again, I wasn't really looking at it for an RV trip.)
Other options:
Keep taking I-25 up to Casper and cut over. That road was pretty good, altho once again watch out for high wind. You'd have to cut through the park to get to the west side.
Take I-25 all the way to I-90. I don't know how far out of the way that takes you, but you get to stay on interstate almost the whole way.
Take I-80 to I-15. Probably further south than you want to go, but again, interstate.
Whichever way you go, I hope you have a lot of time planned for Yellowstone. We spent over a week checking out the park, and still didn't get everything in!