How much time should we allocate to a cross US-Canada road trip? Anyone tried this before?

Three weeks isn't near enough time to drive the whole of Canada and the US. It takes 5 full days to drive across Canada, assuming you drive 24 hours a day. If you actually want to do this and make it meaningful, it's a 6-8 week trip.

Three weeks, no way if you want to actually see anything. Maybe six weeks though. You need to have at least one day to see anything in any of those places, more than that in some of those places. At this point, 20 places in 21 days would already be a stretch - even without taking driving into consideration. Some of your drives are short (e.g. Calgary to Banff, about 2 hours), some are really long (e.g. Edmonton to Winnipeg, about 15 hours). So your first step: figure out the driving time between each place. Then work from there.

I went from Victoria to Halifax in 12 days, seeing very little. Figure 1 day drive between places. Then figure 1 day for each thing you want to do. Then round up to the nearest week. I would do that trip over the entire summer, if possible.

You'll never do all that in 3 weeks.

3 weeks is okay if you don't want to stop anywhere. Otherwise is is MUCH to ambitious. The trip is over 14,000 km, not including a trip up to Edmonton. If you drove about 12 hours a day, the driving alone would be 14 days, at least. That gives no time to see anything, and, driving that much would be horribly unsafe. Even doing this trip in 6 weeks would be really rushed.