[*]We then have a car rented for two weeks and plan to drive to Vancouver Island and spend 2 nights there (we definitely want to go to the Tofino area for whale watching – is Victoria worth visiting too?).
If you have the time to go down to Victoria, it's definitely worth the trip. Be aware though, that it is about a 5 hour drive down to Victoria from Tofino, so you should be prepared to 1) leave early and spend the afternoon or 2) stay a night if you can to have time to enjoy the city and visit the attractions you want. You'll be able to head back to Vancouver with a ferry straight from Victoria (as opposed to Nanaimo when heading to Tofino) so no real worries about having to drive back up.
[*]We then have 8 days/7 nights to drive from Vancouver Island to Jasper National Park. Which route would you recommend for that? Via Whistler or Fraser Canyon? Should we go via Clearwater or further north via Prince George? Or maybe via Kaloomps and Mt. Revelstoke/Glacier National Parks? Any recommendations for a nice place along the way where we can relax for 3-4 days (maybe a lake)?
[*]The next stops will be Jasper National Park (2 nights) and Banff National Park (2 nights). Does that sound like the right length for the parks?
The Whistler/Fraser Canyon route is longer compared to some of the other options but it gives you a chance to visit Whistler. My suggestion would be to spend one of your days in Vancouver to make a day trip up to Whistler (about a 2 hour drive) instead as it should be enough for you to enjoy the village.
Taking the Coquihalla Highway (Hwy 5 -- there is a 10 dollar toll) is probably the best option heading up to the Rockies. If you want to a place to relax along the way, take the Okanagan Connector (Hwy 97C) from Hwy 5 to the Okanagan Lake area (Kelowna, Osoyoos, etc) area. It's a touristy area well known for the lake/parks and wineries. I would personally recommend that you don't stay more than 2 days here and use the extra days in the Banff area. There are a ton of things to visit and experience in Banff and 2 days will definitely be tight.
From Kelowna, you can take Hwy 97 up to Salmon Arm, then Hwy 1 over to Lake Louise. You'll pass Glacier and Yoho National parks along the way and definitely worth a visit. Once you get to the Lake Louise area, you can take the Icefields Parkway (Hwy 93) up to Jasper. Lots to see along the way, including the Columbia Icefield. You'll be taking this route down to Banff again, so it's your choice whether or not you want to see all the stuff on the way up or the way down. Two days in Jasper should be enough for sightseeing.
I should say that we like nature and would like to do a few short hikes, but are not much into activities like rafting, mountain-climbing, etc. Ideally, we would prefer two-night stops over one-night stops.
They're definitely be a lot of short hiking opportunities in all these places with great viewpoints along the way. You'll enjoy them for sure.
I think that answers all of your questions. If you want some more detailed info or have any further questions, feel free to ask!