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As for saves, they go with the Steam account so as long as every player got her own Steam account (and their respective system account which should be the case if they're playing on different systems), you're fine.
After all how are you going to buy a second license of Stardew Valley without at least one child account?
Part of the reason Family Sharing exists is this scenario.
Maybe it seems like splitting hairs, but you're letting your kids use your account already. Ok so create a second and third account for yourself, which you're allowed to do. And let your kids use those. It's the same thing you're doing now, with fewer impediments.
https://help.steampowered.com/en/faqs/view/054C-3167-DD7F-49D4