Family Notifications
My sister is the organizer for the family sharing, but I want to add my child and get the notifications. Would adding a different monitoring app stop her from getting the child notifications?
iPhone 8
I am not clear what you're asking about. What notifications? If you mean Ask To Buy, that is independent of any other app you may be using. Approve what kids buy with Ask to Buy - Apple Support
Note that ATB isn't a monitoring app, it simply requires children to get permission before they can buy something from the iTunes and App Stores.