I'd say a combination of both. Steep hills, switchbacks, stopping for lunch, pictures, etc. The skyline trail is worth it though, the panorama point viewpoint at the top is beautiful. But to be fair, I last hiked it about a decade ago so my memory might be fuzzy.

I would factor in traffic and trying to find parking, that will add more time to the commute, especially in summer. Like, unless you get to the Mt. Rainier gate in the early morning there's going to be a long wait even just to get into the park (like even up to an hour and a half sometimes). Also unless you both are in great shape that sounds like a lot of strenuous hiking, you might not get all those hikes in - I'd pay attention to the elevation gain on these hikes. Last time I hiked the Skyline trail it took me about 5 hours, and I was in average shape back then.

I got the flu shot but now am on day 8 of being sick with the flu. I shudder to think of how much worse it would be if I wasn't vaccinated.