Doable, but is it enjoyable ?!

I second Peach1 suggestion - concentrate your trip into Rockies, Glacier NP and Yellow Stone area and do the Utah portion in a separate trip.

Yellow Stone in Summer time can have traffic jam - though I dont think it takes 1/2 a day to/from West Yellow Stone and Yellow Stone.

On the other hand, all Geyser/Hot Spring areas require some trails, even a very short distance one ... I think only Fountain on Firehole Drive is truly a drive by ...

Keep that in mind, you need to check on the erruption timetable and decide HOW you would like to do - give up the erruption (the prediction can only be a window of 90 min to 4 hours, depends on location) or just drive thru - and without erruption, many Geysers / Hot Springs are really nothing to see ...

The way you plan it, you can only say, Oh yeah, we have been there ... :-)