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EDIT: shouldn't say that sorry
There are many important reasons why each child should have their own account, but the biggest one is to future proof things. They will not be children forever. If you throw all games you buy for your son onto your account, and then put all games you bought for your daughter onto your account, when they grow up, who gets access to their games when they move out? Even if you keep having multiple people violating the SSA by account sharing, the same thing you're describing here can still happen.
The first thing you need to do is make an account for each child. Do this with them because the username can not be changed.
Then you need to set up Family sharing so both of their accounts are able to use games from your library on both computers: https://store.steampowered.com/promotion/familysharing
Then you need to start considering who "gets" what games when you buy them. Is this game a present for your daughter? Buy it for her account. Is this game a present for your son? Buy it for his account. Your Son will always be able to play the game on his account even if your daughter is borrowing a game from your library.
Bonus points if you set up family sharing so your Son and Daughter can share their libraries with each other as well.