Is this too far in too short of time

What's right for Yellowstone is every minute you can spare for it. With a day and limited mobility, that should include at least Grant Village (Yellowstone lake and visitors center), West Thumb Geyser Basin, Old Faithful and the Fountain Paint Pot. All of those are on US-89 which you'd take into the park from the Grand Tetons, and are relatively easily accessible. The best advice I can give on finding the good local eating spots is to ask the locals, particularly tourist information centers and in smaller town halls. Some information centers may restrict how specific the advice can be that is volunteered, so be sure to describe as exactly as you can what it is you're looking for and ask the person where they'd eat if they were looking for such an experience

AZBuck