Stop kids from deleting history?

Sure. Create a separate account on your Mac for each child, and then they will have their own Safari history stored in their respective accounts, and cannot access yours, as long as you are the sole administrator; do not keep that adminstator password where it can be retrieved (or guessed), and do not type it while the children are within view, or they will learn from your key strokes.

The follow karina184's links for placing restrictions on each childs account.

Hello Valasaurus,

Thank you for using Apple Support Communities.

We understand that you want to prevent your kids to delete the browsing history. You can take a look at the following support articles on enabling and using Screen Time and parental controls on your Mac and iOS devices. While there isn't anything there specifically for browsing history, you may find other options that will help with what you want to restrict, like sites or apps.

Use Screen Time on your Mac - Apple Support

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

Best regards.