You don't give your route, so I assume that you will be coming from the south. To have more time in Sequoia, I would suggest a stop in Visalia or Fresno for a day trip to the Park.
I have stayed at the Yosemite South / Coarsegold KOA in Coarsegold, CA before it was a KOA. Not the best, but worked for us at the time because it was free.
Also have stayed at the Bass Lake RV Resort in Bass Lake, CA. Membership park, but I think open to the public.
While eating at the fabulous buffet at the Chukchansi Gold Resort & Casino in Coarsegold, I notice that you can dry camp there for a few days.
If you are going to be on the west coast for any length of time, I would suggest that you look at the
Thousand Trails Zone Pass. You can get two zones for $525. 30 days free camping, then $3 per night. There is TT park just outside Groveland, CA about 5 miles from the Yosemite Park's entrance. Then a beautiful drive into the Valley and the rest of the Park. A weeks stay at a commercial campground would almost pay half the cost.