I'd recommend *not* trying to do YNP and GTNP from a single base. It's 90 miles from West Yellowstone to Colter Bay, with speed limits between 35-45 which make it over a two hour trip each way.
We will usually base camp inside Yellowstone (one of the internal campgrounds if they're still open, West Yellowstone if they're not) and spend at least three days in Yellowstone. You'll never run out of things to see.
Tetons for us is no more than a solid day visit. Unless you're doing some horseback riding or hiking, you might want to keep that short and over-do your time in Yellowstone. Colter Bay has an unreserved section with hookups that worked well for us. Gros Ventre isn't so bad if you're only using it to sleep as opposed to a couple lazy days at a campsite.
