How to prevent child from using Find My to interact with parent's device?
I would implement parental controls on their device. You set a passcode and then you can control which apps are hidden. 


https://support.apple.com/en-us/HT201304


Start with hiding that one app and then see if you want to impose other restrictions. You might ensure iCloud backups are set and lock their iCloud to your family plan as well for extra security in case you lose the passcode or the device becomes locked.  Some people RE prone to try to erase or get around things, so getting a good backup can save you time and grief. 

Also, you can decline to share your location with accounts one by one and let then use the app for other people to share if that’s compatible with your end goal.