I haven't tried this, but if you are using iCloud then you could enable folder syncing in beorg and then share one of the subfolders with the other person - and vice versa.
See https://beorg.app/learning/enabling-subfolders/ for how to enable subfolders (this works for all sync methods except for Box).
I'm interested in a working option from a knowledgeable person as well for your scenario.
So far I can only comment from my side with a small test I just did. I created a new .org file on beorg app with one entry and synced it via WebDAV over to let it create the instance on my PC first. Then I took the iPhone offline. Added an entry from my PC to that .org file (simulating the 2nd iPhone / device so to say), added also a further entry on the iPhone (while still offline). Then switched on wifi again and let beorg WebDAV-sync.
It took over the entry from PC, and lost (respectively did not keep) the 2nd entry made on the iPhone.
So I'm afraid like this it is not suited for collaborative editing on one and the same .org file.
WebDAV though would be technically applicable for 2 iPhones, as you could set it up with the same WebDAV account. But it is just not meant for collaborative editing on the same file. Hence you would need to "coordinate" your and your wife's editing time, which is not practical.
iCloud - I almost never use iCloud, so I'm not sure if the same iCloud account could be used, when both iPhones would (normally) operate each with their separate Apple ID. Even if you find a way to sync specific contents between 2 different iCloud accounts, you would most likely end up in the same situation as experienced with the WebDAV example outlined before.
Now, there might be a small chance of another setup, but I can't test it at the moment, and I just theorize on it:
there is another sync method available in beorg "Choose Folder", and then "Link Folder", where you select - obviously - a local folder on your iPhone.
My idea would be now: if that folder can be put under git control, then conflict resolution could be handled via a git client on iOS. That would still not be a great collaboration user experience, but it would give at least the option to see, resolve, merge conflicts first, without losing data, and then continue.
The said best git client under iOS is "Working Copy". Unless this app and beorg can't access the same folder, then another app might be required to expose such a folder. That app would be "Secure ShellFish" afaik.
That "could" work overall, but someone would need to test it. But again, even if that would technically work out, the "merge conflict and avoiding to lose data"-scenario, which is very likely if multiple people operate on an .org file together, will always happen in a beorg/org-mode setup. Just this git-controlled folder approach would just allow to control to not lose data, but it is still a cumbersome workflow most likely.
The git-controlled folder then needs to be stored also on some server instance, which has to be accessible from both iOS devices. Working Copy can access Github repositories for example, next to own NAS instances, and there is also WebDAV, but I haven't looked into details yet.
David Dreher