Your plan above looks reasonable.
A couple of thoughts - At Mammoth Hot Springs there are often Elk grazing in the grassy area across from the Hotel. The Visitor Center there is in one of the buildings dating back to the 1800's when the army was stationed to patrol the park.
When you drive from Mammoth to the Roosevelt Arch and back again check the hillsides for Bighorn Sheep. We have seen them a couple of times. IIRC there are signs along the road that it's a sheep conservation area.
The Lamar Valley is the most remote portion of the Park with little in the way of facilities. There are toilets just beyond the junction of Soda Butte Creek and the Lamar River and also at the turn off for the Pebble Creek Campground.
If you are interested and have the time, we usually see Mountain Goats on the sides of Barronette Peak beyond the Lamar Valley up near the Northeast Entrance. Binoculars are a must - otherwise they are just white dots against the gray cliffs.
There are 5 Mountain Goats in this picture. Mother with two kids upper center and mother with one kid lower right.
Forgot one other important thing. Be very careful if you need to drive after dark to get back to the campground. The Bison in particular like to walk the roads, especially in places where the level surface makes travel easier for them.
