Your style will decide how many parks.
Hi and Welcome to the Great American Roadtrip Froum.
You have a pretty good take on the layout of the country and a good grip on what you want to experience with your wife. Regardless of what you do, it will be a great trip. As to how much and what you visit will depend very much on your style of travelling.
What I would do is route from LV to Zion, Bryce and then via UT12 - The Million Dollar Road - to Capital Reef, then onto Arches and Canyonlands near Moab. Take UT128 from I-70 into Moab, it is a spectacular drive through wonderful country. Then through Monument Valley and onto the Grand Canyon via the East Entrance - entering the canyon along the Colorado River. How long you like to stay at each of these parks, and whether hiking is part of your enjoyment, will depend on whether DV and Yosemite are then on the menu.
As a guide I would allow at least a day or two at each of Yosemite and GC, a full day for Zion (if you are into hiking). Bryce can be seen in half a day, unless you like to go hiking down in the canyon among the hoodoos. Same really goes for the other NPs.
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Would Death Valley be interestingly different after the hot canyon country?
Death Valley is an amazing and unique landscape, definitely worth your time, even if you only drive through it. Note that will be hotter than the canyon country. It is the lowest, hence the hottest part of the States, but that should not deter you. A drive in your air conditioned car with ocassional stops for a photo is definitely doable in summer. Carry lots of drinking water.
You're likely to get respite from the heat in Yosemite, especially the Tioga Pass area, which is high up in the Sierras.
Lifey