Best Switch User Setup for Family with 2 Users and 1 Account

We have 2 Nintendo Switch devices in our household for our kids. I'm the user account holder, who's paying for Nintendo Online (through a broader family account I should say). Havoc broke loose when my daughter's progress on Rayman was reset because my son played on 'her' Switch Lite. Upon checking, the Switch Lite only has myself as a user, so they both have been using mine. On the regular Switch, I also have a user profile but so have both my kids so on that device, we don't have those issues. On the Switch Lite, when trying to add users (my kids), it asks me to link it to a Nintendo Online account and when I try to do so, it says I'm already set up. How do I get both kids to have their profiles on the Switch Lite, like they have on the regular Switch (so under my general account)? The main purpose is that they can save their own progress when playing under their own user account, I don't mind that they can't play the same (online) game at the same time.