In your Mac you as an administrator has signed with your Apple ID and password and can view your iCloud data ( could be photos ...) , your wife is using a different iPad / iPhone and having a different Apple ID and password .
To view her iCloud data , in your Mac open a new tab ( use command and T keys ) and she has to sign her Apple ID and password at www.icloud.com ( she can remove pictures from her iCloud account see the article https://support.apple.com/en-in/guide/icloud/mm08b49040b5/icloud
To add photos in albums see the article https://support.apple.com/en-in/guide/icloud/mmfedd89eeca/icloud
Creating a new admin account can be done in users and groups , so you have to first log out from Mac and then she has to sign in with her admin name and password , in the same way open a new tab and view photos / delete / add to share albums at www.icloud.com
It's your convenience which way to delete / add to share albums the photos .