I'd definitely recommend flying from Vancouver to Calgary. It's a long drive - we've done it twice, once flying and once driving, and definitely felt that flying was better - there's so much amazing scenery to see so it's a shame to have to spend time driving through less exciting stuff.
We're not great city visitors so we spent minimum time in Vancouver then got the ferry over to Vancouver Island where we spent a magical time at Tofino ( Crystal Cove if you have family have great lodges with hot tubs) and also a few nights at Whistler.
In Vancouver we stayed at the Sylvia Hotel in a family room. It's slightly old-fashioned, but reasonably priced and loads of room in the family room and the hotel is in a great location right beside the beach.
For the Rockies I would avoid staying at Lake Louise - it's ridiculously crowded in the summer and the accommodation is very pricey. Definitely worth a visit though. Arrive very early to get parking and do the canoe trip for half an hour and hike up to the tea house.
Banff has lots of accommodation including quite a few aparthotel places which would be good with DCs.
If you go to Jasper, then avoid eating at the Ice House parkway stop like the plague. It's disgusting. I also wasn't hugely overwhelmed by the glacier bus trip - if you want to do it book in advance. Also avoid the skywalk - overpriced and unnecessary, with beautiful view points a couple of miles down the road for free.
We loved Canada. To be honest with only two weeks and young DCs I'd probably cut down a bit on the trip to reduce travelling. Our DS was 10 when we went but he really loved Tofino and Whistler, but was a bit less excited about the Rockies - guess DCs aren't as into scenery.
I'd maybe skip Jasper for this trip- it is a scenic drive, but it is a 4 hr drive each way without stops. I say this trip as once you've been to Canada you'll be hooked.
I booked our accommodation around this time for a trip in July and was able to find what we needed, but the absolute prime spots tend to go quickly.