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On your Mac, you have one Applications folder stored on /Applications, and applications stored there shows on all users, and then, each user has got an Applications folder on ~/Applications, where you must save the apps that you want to show only on one user.
In your case, log in your kids user. Then, open Finder, choose the applications you want to show only on that account with Command key, go to Edit menu and select Copy.
After that, go to Go menu > Go to Folder, and type ~/Applications. Finally, right-click on the Finder window and press Paste, so applications will appear on that folder.
Also, to delete those applications from /Applications, choose Applications on the Finder sidebar, select the applications you copied to ~/Applications, and move them to the Trash. After doing this, those applications will only appear on your kids user