How to block kids from downloading previous apps

Hello Sunshine1008,

Thanks for that info and for choosing the Apple Support Communities. If we understand correctly, you would like to prevent kids from reinstalling apps that are in purchase history already. To do this, please do things like hide the apps and use parental controls by enabling Screen Time and then going to Settings > Screen Time > Content & Privacy Restrictions, enabling this feature and then tapping iTunes & App Store Purchases, tapping Installing Apps and switch this to Don't Allow and here is more info:

Hide purchases from the App Store

Use parental controls on your child's iPhone, iPad, and iPod touch

Cheers!