Family Sharing iPhone - Unique Question about purchases
Yes. Sign up for a free MDM solution and enroll your child's iOS device under management. 


add the app(s) in question to management


You then get telemetry and reporting if that app is installed. 

I prefer JAMF now, but there are several options. I’d start with this and then research others once this one has some specific drawbacks for you. 


https://support.jamfnow.com/


You won’t need DEP or VPP to run family devices under management.