I'm not Mary Jo...but I know a bit about Yosemite, also.
Where are you staying - will you actually be in the Valley or will you have to drive in from somewhere outside? Most of the things I talk about below can be accessed from the Yosemite Valley shuttle, which is free, so if you're coming in from outside of the Valley you can park in Day Use parking and catch the shuttle from there, and of course the shuttle services all of the various lodging and campground areas in the Valley, so you're already set if you're staying there.
When are you going to be there? During the summer? (Summer in the northern hemisphere, that is!) Late spring? Fall?
How much walking is the four-year-old able to do? My idea of a "major hike" might be rather different than yours.
One thing that we've enjoyed doing when the river is high enough is renting rafts at Curry Village and floating down the Merced River. It takes a couple of hours - they pick you up where you get out and transport you back to Curry Village in a bus.
Visit one of the sequoia groves - if you go to the Mariposa Grove there's a tram tour you can take (so less walking for the 4-year-old), whereas the Tuolumne Grove is less crowded, but it's a mile+ walk each way - and it's uphill all the way back.
If you're actually staying in the Valley, make sure you see some of the nighttime "ranger" programs - there will be a schedule in the newspaper you get when you enter the park. Sometimes they show movies, sometimes slides, sometimes they talk about animals, etc. There are also programs during the day that are geared towards kids, which might work out well for you.
Visit Lower Yosemite Falls - that's a short walk, though there's a little bit of a climb. It's a loop that goes into the woods a little bit. Probably 1/2 mile total.
Take the short walk to the base of Bridalveil Falls.
Visit Mirror Lake - that's a longer walk, up a steeper hill. But that's a good place to go for a picnic - there's some nice sandy beaches along the "lake". (The lake is turning into a meadow.)
Rent a bike and ride on the 7+ miles of bike paths. It's a great way to get around the Valley. I believe you can rent a kid trailer to pull behind the bike.
Visit the Nature Center at Happy Isles - it's a short walk from the tram stop to the Nature Center, and you can also take a short walk onto the islands in the middle of the river. There's also a walk through the fen on a boardwalk. IF the 4-year-old is up for it, take the trail from Happy Isles to the Vernal Falls bridge - it's about .8 miles, but the trail, though it's paved, is rather steep. You get a very nice view of Vernal Falls from there.
There's several things to do at the Visitor Center - I suggest seeing the movie about Yosemite, which is very well done. There's also a museum and the Indian Village there.
Hope that helps!