Separating linked Apple Accounts and resolving privacy issues

I need to resolve how to separate my two ID accounts which for some reason got linked and are creating problems. Few years ago we activated home sharing to watch movies at home and then turned that off, but since then, I am getting access to the info of my husband account - photos, passwords etc, and he of mine. We have tried everything to check if the accounts are connected and are unable to solve. Please help and advise about how to make each account independent and have privacy matters resolved.

[Re-Titled by Moderator]

Original Title: Separating Apple IDs