apple account keeps getting locked

Mike_OR wrote:

All devices are in my possession, except for my wife's computer, which is part of our "Family" grouping.

So, is your Apple Account signed into that computer where you are listed as the Organizer?

It may be best to have your wife create or use her own Apple Account on that computer where she is the Organizer and you are listed as a Parent to manage your Family Sharing. Some actions on that computer will require your Apple Account password, which would have been changed after the unlocking. A previously saved password on the computer will fail and after multiple attempts, your account will be locked.

No one from Apple is here to respond to a support question, so if you want to speak to Apple directly, then you can use the number found in this link:

Contact Apple Support - Apple Support

My recommendation would be to change your Apple Account email used to sign in.

Change your Apple Account primary email address - Apple Support

Are your other devices being used by someone that knows the Passcode to unlock those devices. If a family member or someone else can access the device and attempt account access with the unknown password, it will lock your account.

Review the devices that can sign into your account to make sure they are all accounted for at Settings > [name on top], and scroll to the bottom. For example, if you signed into Apple TV at a hotel, that TV may still have your account login and other guests may be trying to access your account. You would be able to remove that TV from your account if it is found in your Settings, although the email address is likely still stored on the TV.

Mike_OR wrote:

…But this is where I find Apple's interconnected system so confusing. We are sharing content (apps, media) when possible. And we share a calendar. Does my computer even need to have her Mac book listed in my connected devices for these tasks?

Nope.

Family Sharing provides most or all of that, without sharing passwords.

Family Sharing - Apple

Share iCloud calendars on iPhone - Apple Support

You can certainly share content with Family Sharing and Calendars without using the same Apple Account. In fact, Apple recommends that each family member should be using their own Apple Account.

Make sure that each family member has a unique Apple Account - Apple Support

It does not appear that the links provided by MrHoffman came through, so I will also include them here:

Family Sharing - Apple

Set up Family Sharing - Apple Support

Share iCloud calendars on iPhone - Apple Support