I live in California.
Yosemite is spectacular any time of the year, but April is a bit early. The falls will probably be running, but will not be full. The flowers will not yet be blooming in the valley. And the road to the high country will be closed by snow. I remember trying a visit there in April years ago, and was very disappointed.
And you will really be too early for Kings Canyon/Sequoia National Parks. The big trees are at around 7000 feet. Snow will probably be everywhere, restricting hiking in the groves.
The two train trips between San Francisco and L.A. are not very interesting. Same for train from L.A. to Las Vegas. On that latter route, for method of getting between the two places, price rules. Most intercity trains in the U.S. are not very frequent, and are almost always late, sometimes very late (up to a day).
I recommend driving the coastal route, State Route 1 as long as you can stand the 2 lane very winding road driving on the wrong side all the way. (Freeway US 101 more or less parallels it if you get tired of Highway 1.) Highway 1 features very spectacular coast line, Solvang (nice Danish town Danes say is more Danish than Denmark), Hearst Castle (don't miss this amazing place), and the Monterey Peninsula. Don't miss the Monterey Aquarium. Big Sur, south of Monterey, has some nice hiking, as do all of the Redwood State Parks between Monterey and San Francisco.
Do the math before you buy the annual National Parks pass. Yosemite is $20 (per car, not per person), but others are less expensive. You can get prices
here.
Las Vegas has both very cheap and very expensive lodging available. I don't see the point of the latter, since I spend time in the room only to sleep and bathe. I have spent more time than I care to think about in that city (hint: Bellagio and Mirage are the two best places to play poker). I have written up some suggestions for the place on my website,
The Personal Travel Experience of Gary Steiger. I think you will find them useful.
RE: Your idea of driving down to California from Vancouver. I think you can expect a lot of rain. The weather patterns change dramatically around 100 miles north of San Francisco. Better south, worse north. Rain will obstruct views of most of what you would want to see, though the Redwoods can be very nice in rain and mist.
If you rent a car, you will want to return your car to where you rented it. One way rentals in the U.S. are very expensive. So that probably means renting the car in L.A.
There is no way you can see everything you want to see in the short time you will be here. Consider it an "overview" trip, and plan to come back to see the rest. If you are sure you will come back in the late spring, summer or early fall (say late May to mid-October), leave Yosemite to then, especially if you can enter from the East over Tioga Pass in the summer. But if this will be your only trip to the Western U.S., Yosemite is a must.