OK, here is a suggestion. Some people on the forum think I go in to too much detail, but that's me. Feel free to adjust as you like, it's your vacation!
Here is a link to the park map you will get when you come thru the gate.
Friday: Arrive from Grand Tetons. You will want to get to Canyon before dark, and since it looks like you are camping, you will probably need time to set up. It is 43 miles from the South gate to Canyon, so in Yellowstone you double your miles to get approx time, without wildlife jams. So count on 1.5 hours at the least of drive time. Keeping that in mind, if you have time, stop at West Thumb geyser basin then head north. After you set up, I would head back down thru Hayden Valley, which you just drove thru, but this time you can probably stop easier. If you have time, do Mud Volcano and Fishing Bridge (park, get out and walk across), Le Hardy Rapids on the way back. Go to the Visitor Center if you have time.
Saturday: Today is your Canyon day. Go to the Visitor Center if you didn't do that yesterday. If you can be on the South Rim viewpoint called Artist Point at 945, there is a rainbow at the base of the Lower Falls. Do the other viewpoints on South and North rims. If you didn't do Mud Volcano, Fishing Bridge and LeHardy Rapids, head south thru Hayden (it is good to go thru here many times!!) and do them. If you did do them yesterday, head north over Dunraven Pass to Tower Fall and out in to Lamar Valley.
Sunday: Make this your geyser day. Head to Old Faithful via Norris and Madison. After Madison Junction, cross the Gibbon River Bridge, then turn right in to Firehole Canyon. Rejoin the main road. Go south and pass by the other geyser basins you will see, heading for Upper Geyser Basin and Old Faithful first. You will do these others on your way back to Canyon, as I recommend retracing your steps. At Old Faithful, go to the Visitor Center, write down the eruption times of predictable geyser on the brochure available at the desk (50 cents) and see if you can work them in to your walk thru the geyser basin. Starting at Old Faithful, I usually go behind Old Faithful by walking on the boardwalk to the left and ending up at the bridge crossing the river behind OF. This take you to Geyser Hill, from there down to Grand, then on to Morning Glory pool. (Pit toilet down here) Return to the Old Faithful area. I usually eat lunch at the Lower General Store which has gas pumps out front and is the one you will come to when returning from Morning Glory. Also leave room to eat ice cream. I like the huckleberry you can get at the OF Inn on the 1st floor and take it up to the 2nd floor deck overlooking the geyser basin. After you are finished with this area, retrace your steps toward Canyon, picking up Black Sand, Biscuit, Midway geyser basins, doing Firehole Lake Road, then Fountain Paint Pots. Return to Canyon.
Monday: This is your long drive day! Head north from Canyon over Dunraven. Do Tower if you didn't do it before. At Tower Roosevelt, turn right and head in to Lamar Valley. Return to the junction, then head toward Mammoth. Do Petrified Tree and drive the Blacktail Plateau. Do Mammoth, lower terraces, the Visitor Center and look at the old Ft Yellowstone buildings if you wish. Bathroom wise at Mammoth the best ones are the new ones by the gas station where the bus parking lot is. There are some at the Visitor Center accessed by outside stairs but they are very small stalls. Yuck. From Mammoth, head south toward Norris, then back *home*.
Tuesday: As you exit the park, stop by Norris Geyser Basin. The parking lot is quite big here, so should have no problem if you are pulling a camper. After you head west from Madison Jct, watch for bison, elk, trumpeter swan (right after you cross the small bridge, you can often see one in the river which will now be on your right.), and look in the trees for bald eagle.