Sunshine a challenge.......well, it depends. The greens are really flat. The blues are very tame and no tougher than the blues here in the east. And the blacks aren't bad either, especially if you ski Smuggs and Sugarbush. (I've been to Sugarbush). Skiing the east is more about rain, ice, etc. Skiing the west is more about finding the terrain you want.
Thing about Sunshine is that time of year, the "challenging" stuff might not be open (Wild West, Delirium Dive). I'm not a snow forecast expert, but I think it's iffy based on history.
As for Lake Louise, DEFINITELY go there. Honestly, I'd do Sunshine 1 day, Lake 2 days. BUT.......depends on the snow. Don't listen to anyone who says the Lake is "icy". They don't know ice like us easterners. Their idea of icy is our notion of packed powder. Snow conditions at the Lake will likely be moderate coverage at that time, but the views are breathtaking, and you should have some top to bottom runs. Hard to say if the back bowls will be open, but the chances the Lake bowls will be open is likely greater than Delirium open at Sunshine.
Don't hit Banff without hitting both resorts. Do Sunshine and Lake Louise, you won't be disappointed (even if it's low snow it'll still be better than VT). Pass on Norquay, it's a locals hill and not worth spending time there if you only have 3 days, trust me. You can do nighttime snow tubing at Norquay though for something different. And be sure to hit the Upper Hot Springs in Banff. Buses are free and shuttles are included with your Big 3 pass.
Once in town, you literally do NOT need a car. Especially if you're taking a shuttle from Calgary airport? A car will sit there, seriously. Might be easier for you to take the shuttle to/from Banff. You can enjoy the postcard views around every corner, and let someone else do the driving there. The scenery will blow your mind.
Plenty of places to stay in Banff, just find something for your budget/wants/needs. Most are on the main strip, all have shuttles to the slopes at the front door or literally a 2 minute walk to the shuttle.