Thanks for reaching out to the Apple Support Communities.
I understand that you accidentally connected to your family member’s Mio Global Fuse, and now it automatically connects with no option to forget the device. I'll be happy to help assist you with this.
I suggest a close of the Settings app and a restart of your iPhone. It looks like the Settings app isn't responding like it should, because you should see this icon next to the device . That is what you tap to get the option to 'Forget this Device'.
How to force an app to close on your iPhone, iPad, or iPod touch
Restart your iPhone, iPad, or iPod touch
Let me know if this helps.