No. Mud Volcano is in the southeastern part of the park, Grand Canyon of the Yellowstone is northeast near the center, Old Faithful and the main geyser basins are on the southeastern side of the park, and Norris Geyser Basin is on the northwestern side of the park (not too far from Mammoth Hot Springs). As originally scheduled, you were doing most of the southern loop and half of the northern loop in one day. That’s not practical! That’s why I suggested at least two full days to explore the park, and even that’s going to be rushed. Here’s my suggestion:
Day 1: Drive from Cody to the East entrance. Visit the Mud Volcano area, then drive south past Yellowstone Lake and West Thumb Geyser Basin to Old Faithful. Don’t worry about timing your visit to match Old Faithful’s eruptions; the geyser erupts so frequently you’re not going to miss it. Believe me, you’re gong to want to spend a LOT longer than 90 minutes exploring the Upper Geyser Basin. There are two full miles of boardwalks here, and dozens of geysers, hot pools, and other thermal features (many far more visually impressive than Old Faithful), as well as the colorful banks of the Firehole River. Stop by the visitor’s center when you get there, find out when the predicted eruption times for Old Faithful and the other big geysers are, and try to be near them when they go off. When you finish at the Upper Geyser Basin, dive north on the southeast part of the loop road and visit the Middle and Lower Geyser Basins to see the paint pots and Grand Prismatic Spring. Then head for West Yellowstone and your hotel room.
Day 2: Drive from West Yellowstone to the Grand Canyon of the Yellowstone by taking the center loop road east. When you finish there, you have two choices of route: drive back west the way you came (faster), or continue east to Hayden Valley, then north, then west through Lamar Valley (much longer but more scenic, and this is the route that gives you the best animal sightings in the park). Once you’re back on the eastern side of the park, head for Norris Geyser Basin. After your tour of Norris, drive north to Mammoth Hot Springs, then exit the park via the North Entrance.
That’s one day for each half of the park. Rushed (very!), but you’ll see most of the big sights.
Edited to add: Twoflower’s proposed route in post #34 is good, too. But in any case, think of dividing the park into two segments (either north/south, or east/west) and seeing one segment each day. You may have to take into account road closures as well.
Leave from Cody as early in the morning as you can; the drive to the park is about an hour.
I’ll be happy to help you with any additional questions!