Congratulations on getting 4 nights at Yosemite Lodge. Those reservations are very difficult to get. You will certainly enjoy your time in Yosemite Velley, with time to explore the Glacier Point and WWona areas, and maybe Mariposa Grove of sequoias as well ( but maybe redundant if you are going to Sequoia NP).
Note that Mammoth and Sequoia NP are in opposite directions from Yosemite Valley. Mammoth is on the east side of the Sierras, just off highway 395, but there is no road access into Swqupia NP from that side. Hiking involves a long Nd strenuous hike over a high-elevation pass into the wilderness areas of the park.
To reach the “front country” side of Sequoia and Kings Canyon NP (where you find roads and lodges) , you exit Yosemite by the South Gate at Fish Camp on Highway 41 and drive almost to Fresno to reach the road into SEKI from the west . From Mammoth, you would drive up Highway 395 to the Tioga Road (highway 120), then drive over Tioga Pass (a spectacular drive) and through Yosemite. via Tuolumne Meadows. Continue on 120 west to Crane Flat and then down to Yosemite Valley, meeting highway 41 at the Valley floor and turning south there.
That is a lot of driving, but it is all beautiful, and you will have an opportunity to see the high country features of Yosemite, such as Tenaya Lake and Tuolumne. This is actually my favorite part of Yosemite, especially for hiking. It is much less crowded than the Valley.
Note that you can also reach Sequoia NP from Mammoth by driving south on 395 past Bishop and Lone Pine, around the southern end of the sierras and up through Bakersfield. That is the “winter route” but it is very hot (partially through desert) and much less scenic. I do not recommend going that way in summer.
The eastern Sierra is known for beautiful golden fall colors, but September is too early for that.
Mammoth offers a large number of accommodations, from luxury hotels to ski condos and cabins in the town (named Mammoth Lakes although not at the lakes) and on the mountains itself, to rustic (sometimes very rustic) cabins on the lakes themselves. There are 4 lakes with cabins/fishing resorts (Mary, Mamie, George, and Twin Lakes) and most have minimum stay requirements from 4-7 nights. They also book up a year in advance and are rarely available after that, at least not during the main season. We scored one in October a few years back.
The exception at the lakes is Tamarack Lodge, a large complex with a main lodge and separate cabins on Twin Lakes. You can usually get a room in the main lodge or a rustic cabin there in September, in the range of $200-$260. The nicer, more modern cabins are considerably more.
https://www.mammothmountain.com/plan-your-trip/mammoth-hotels/tamarack-lodge#accordion
If you would like to be closer to town, on the mountain, or in town, you will find a huge variety of options listed on websites such as Visit Mammoth:
https://www.visitmammoth.com/hotels-lodging/
Or try the Mammoth Mountain lodging site:
https://www.mammothmountain.com/plan-your-trip/mammoth-hotels
My sister and her family, who go to Mammoth each summer and winter,like the Snow Creek complex; we stayed in a condo with them last July.
https://www.snowcreekresort.com/
Many of these places will not have their summer availability up yet as they are gearing up for the winter ski season. You will have no trouble finding a place to stay if you wait until next March or April (unless you want to stay at the lakes).
What places did you find with such poor reviews?