How do I use a personal iCloud account to share only certain files?

I have a MacBook Pro that I use for myself and an iMac that the family can share. I have several apps (i.e. Chronicle and iBank) that incorporate iCloud back-up.

How do I set up a Family Sharing account that ONLY shares those files. I don't need to share my email, my calendar, notes, etc.

I tried setting up a separate iCloud account that the family could use. However, when I went to sign in to my iPhone (with my personal iCloud account), the fact that I wasn't logged in to that family iCloud account, none of the files got updated. I don't want to keep switching iCloud accounts.

Is it possible to share those files (only) on my personal iCloud account to other devices (the iMac, etc.)