3 Days in Sequoia + Kings Canyon
Three Rivers worked well as our base, but the decision that made the trip was giving Kings Canyon a real day instead of treating it as the secondary park.

The short version
Use one day for Sequoia's giant trees and Moro Rock, one full day to drive deep into Kings Canyon and hike Mist Falls, and keep the third day flexible for another hike or anything you missed. If you only have two days, we would still protect one Sequoia day and one Kings Canyon day.
Day 1: Giant Forest + Moro Rock

Start with General Sherman and Congress Trail. The famous tree is the headline, but Congress Trail turns the stop into an actual walk through Giant Forest rather than a photo-and-leave experience.
Later, do Moro Rock. We went very late, when it was not crowded. The climb is steep, but the stone steps and railings made it feel much less scary to us than the exposed setting might suggest. The Great Western Divide views are an enormous payoff for such a short hike.
Our original trip planning also included Tokopah Falls and optional Little Baldy. We would treat those as flexible rather than forcing every planned stop into the day.
Day 2: Kings Canyon Scenic Byway + Mist Falls

This is the day we would not compromise. From Three Rivers, the drive to Grant Grove alone is substantial, and Cedar Grove is farther. But the Kings Canyon Scenic Byway was part of the experience, with huge canyon views along the way. We also liked using GuideAlong on the drive.
Continue toward Road's End and hike Mist Falls. This was our favorite hike of the trip because it combined the canyon, river, waterfall, wildlife and a much wilder, less crowded feel than the major Sequoia attractions. We saw very few people compared with the famous-tree areas.
Grizzly Falls and Roaring River Falls are easy roadside additions. If you still have time and energy, add a short Zumwalt Meadow stop.
Day 3: Big Baldy or missed Sequoia stops

Use the third day as a buffer rather than creating another rigid checklist. Big Baldy is a good moderate ridge option if you want another hike. Otherwise, return to Sequoia for anything you skipped on Day 1.
If you only have two days
Day 1: General Sherman + Congress Trail and Moro Rock. Day 2: Kings Canyon Scenic Byway + Mist Falls. We would not cut Kings Canyon simply because Sequoia has the more famous name.
Where to stay
We based in Three Rivers. It is convenient for entering Sequoia, but understand the tradeoff: a Kings Canyon day from there involves real driving. For us, that was still worthwhile because the drive itself became part of the sightseeing.
Beyond the Overlook