Lots of choices out there for youth model shotguns. find one that fits your kids. This will make a big difference in their ability to shoulder and shoot effectively.
Ground swatting vs wingshooting...another challenge altogether.
As mentioned above, how and where you hunt birds may have a significant impact on the opportunities your kids will have learning to hunt and kill birds. Road/trail hunting birds in thick forests and mountain areas, or open prairie/grassland, or semi-open aspen stands. Many different environments that people hunt birds in across Canada; what works best in your area?
Nothing wrong with letting kids get comfortable with groundswatting birds (of any type that the chosen gaige and shot will effectively bring down with the various chokes). And then it comes to small game, those targets usually aren't flying anyways! LOL (Although squirrels running through the treetops can be a challenge!)
When you're ready for them to learn skeet/trap/clays to learn how to wingshoot, at least they'll have the basics in handling and aiming down...and then they can work on the next level skill. This is where a larger gauge may be more effective and therefore enjoyable vs frustrating for the youngsters. Then again, there are those that have better natural ability than others and wingshooting of any type just comes easier to them than others. Here is where proper instruction is going to make a huge difference in their progress.
I started with a Winchester Model 37A in .410 as a kid, using 2 1/2" 7 1.2 shot. Shot lots of grouse and snowshoe hares on the farm. In the dark spruce and semi open aspen, I never had many opportunities for wingshooting, and meat for the family table was the priority, and as a 10 year old, waiting for a bird to be still, whether on the ground or perched in a tree, was the more effective way to ensure it was brought to bag. I hadn't hunted grouse with a single shot for many years, until I went out one afternoon with a friend, and we used his old Cooey 84 with 3" 7 1/2 shot to take a number of ruffies. What fun! Brought back a lot of fond memories of hunting the farm with Grandma. I went looking for one...
Today, I have a Winchester Model 37A in 28 ga, as I wasn't readily able to find one in .410. I have really enjoyed the 28, and ammo hasn't been that hard to find, and when I do, generally less expensive than .410 today. I have had a lot of fun hunting grouse with it, and my Remington 1100 Sporting 28, which my wife claimed, and a Benelli Ethos, also in 28. We use 7 1/2 shot in all of these. (I have bought some 4 and 6 to try on ducks and pheasant (if/when I get another chance to hunt southeastern Alberta). I really need to get out to the range this summer on the evenings when they are shooting clays and get some lessons on wingshooting!
I had also found a Cooey 84 in 28 ga, that my daughter now has, and a Cooey 84 in .410 which I gave to my mother. Neither of them wongshoot.
Recently, I found a Youth model Winchester Model 37A in .410 and have bought it for future grandkids.