Both Banff and the Kananaskis are easy day trips from Calgary. We do it all the time. However, if your focus is the Rocky Mountains, then I agree with the suggestions to stay in Banff or Canmore.
Radium is a 3ish-hour drive from Calgary. We used to often go for the weekend, but I agree that 1 night is too short. Radium is a beautiful hot springs--built right against rock cliffs--and it has a cooler swimming pool that kids enjoy, too. It is very common to see big horned sheep around, even right in the town. There WILL be some twisty roads (but paved) between Banff and Radium, but most of it is relatively straight. Some other places to visit near Radium include the town of Invermere (really cute town, with a lake and beaches), and Fairmont Hot Springs (which were my favourite as a kid). On the way to Radium, you would pass Castle Mountain (spectacular!! My fave! Note: you would pass this on the way to Lake Louise, also.), and the Paint Pots (an easy hike).
The drive between Banff and Jasper is very long--longer than you'd think by looking on a map. Yes, it's on paved roads, but there are high passes and slow areas, and there are sights to see and stop at along the way. So, plan on spending at least 5-6 hours on that drive, if you choose that option. If you want to start in Jasper, from where would you be arriving into Jasper? Edmonton? That's a bit of a drive, too--much longer than Calgary to Banff (i.e. 4-5 hours). Personally, I wouldn't choose that if I had only 5 days in total. Also, Jasper is quieter than Banff, and there are some beautiful areas nearby, but the town itself and the surrounding mountains are nowhere near as pretty as in Banff.
If you go to Yoho, I suggest going to Takakaw Falls. They're spectacular. Be aware that the road from the highway has twisty sections, though.
A relatively inexpensive but decent place to stay in Canmore with a family would be the Rocky Mountain Ski Lodge. https://canmoreskilodge.com It's got apartment/loft suites large enough for families. It's nothing fancy, but it's comfortable.
In Banff, I like Hidden Ridge Resort. It's actually a little bit outside of the main townsite, on Tunnel Mountain. It also has apartment/loft suites, has a couple of large outdoor hot tubs, and you are highly likely to see deer or elk munching on the grass around there. https://banffhiddenridge.com
Another option we like is to stay at Johnson's Canyon. They have cabins that are a bit rustic, but give you a good amount of space: https://www.johnstoncanyon.com
Our son and his wife frequently rent a condo via Air BnB in Dead Man's Flats or in Canmore, so that's another option for a family.
Be aware that, in the past, both Lake Louise and Johnston's Canyon have been crazy busy in the summer--so much so, that we gave up even trying to go. We enjoyed visiting both during Covid. I'm not sure if all the tour buses have returned yet, so it might not be as bad this summer, but I, personally would avoid those places. (Although I've seen them before. I know that, for some people, Lake Louise is a "must see.") My choice would be Banff area and Radium for a good taster of what the Rockies have to offer.
Be aware that there are two seasons around here, especially in the mountains: winter and construction. You almost certainly WILL be slowed down by construction on the highways.