@Maoira That's part of what I was trying to say, but maybe I was unclear. I also did some additional digging.
Yeah it might actually be possible to change to a 7-speed, but because of having to change other parts besides the hub too, it's probably more money and headache than is worth it. If it were me I'd just replace with another 6-speed if it gets worn out as it moves through the kids (changing the chain regularly will of course help it last longer).
The product page for the Rev20 lists the rear cogs as "Shimano Tourney, 14-28, 6-speed", and based on this and images, it seems like it is this https://bike.shimano.com/en-EU/product/component/tourney/MF-TZ500-6.html on Shimano's site. This is a freewheel, which means there is no freehub at all, and no cassette of any speed is compatible, they're two totally separate ways of implementing rear cogs. I'm just going off these webpages though, @REI-JimL and @REI-AlyS suggestion of firstname.lastname@example.org could definitely tell you for sure if this is correct.
There are freewheels that come in 7 speed (it's rarer to find 8 speed freewheels), and they would probably thread onto the wheel just fine as it's a standard threading. After doing a little more research, there actually probably is a good chance too that it would fit back into the frame, since the spacing between cogs on a 7-speed is often 0.5mm smaller than a 6-speed. Again, email@example.com could give better assurance for whether any specific freewheel would fit in the frame and any other compatibility issues. Would still need a new rear shifter and rear derailleur though to be able to access the 7th gear, that's unavoidable.
Lastly, would you want 7 speeds for your kids to go faster in a harder gear, or to climb hills easier in a lower gear? Because you're unlikely to find much for going faster: the highest gears are those with the fewest teeth (in back anyways), and those rarely go below 13 or 14 teeth on freewheels. Going up to 7 speeds is much more likely to give you an extra lower gear for climbing, with your high gear unchanged. So depending on what you want, "upgrading" may not even get the result you're after.
A lot of information, I know, but I hope it helps!
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