Hi - Since you mentioned your apple ID, I'm assuming you want to use iCloud.
The best (in fact pretty much the only) way to do this is to set up a photos library on the external drive that you both use as your system library.
First you need to move the library to the external drive. Make sure FIRST that it is formatted correctly (APFS or MacOS extended)
For details see:
https://support.apple.com/en-gb/HT201517
Then you are each going to need a user account on the mac (You already have one, you'll need to set up one for your wife, and set up her apple ID with that account.
Then on each account, open the external library and set it to be the system library (in photos preferences), then enable iCloud photos - if not already.
Then when photos is open in your account, it will sync your phone photos to the library. Similarly when photos is open in your wife's account it will sync her photos to the library. You will both have the others photos on your phones (everything will be synced)