It sounds like you and your dad are sharing the same iCloud account (you are both logged in to the same iCloud account.)
You and your dad should be using separate iCloud accounts. iCloud accounts, because they are designed to sync personal data between a person’s personal devices like a person’s computer and iPhone, should be individual.
I suggest that one of you create a new iCloud account and use that one instead of the shared one. Then data like bookmarks, contacts and calendar data will remain separate. Once that is done then you can trim/delete any bookmarks that you don't want.