Hi there LilBang,
The item you're seeing in Activity Monitor isn't related to Family Sharing, but is most likely leftover from the app you uninstalled. You'll want to start by making sure you fully deleted the app with these steps:
Use the Finder to delete an app
1. Locate the app in the Finder. Most apps are in your Applications folder, which you can open by clicking Applications in the sidebar of any Finder window. Or use Spotlight to find the app, then press and hold the Command (⌘) key while double-clicking the app in Spotlight.
2. Drag the app to the Trash, or select the app and choose File > Move to Trash.
3. If you're asked for a user name and password, enter the name and password of an administrator account on your Mac. This is probably the name and password you use to log in to your Mac.
4. To delete the app, choose Finder > Empty Trash.
You'll find this information here: How to uninstall apps on your Mac - Apple Support
After following those steps, try performing a search in Finder on your Mac for any other files related to 'family.app' and try dragging them to the trash. Learn more about searching on your Mac here: Narrow your search results on Mac - Apple Support
Take care.