I have not implemented a solution to this, but it's been on my radar for a while. The two best options of which I'm aware are:

1. Export a .ics file based on your agenda (support for this is built-in) to a shared folder to which your spouse has access (syncthing/dropbox/whatever). Your spouse would then use their calendar app to subscribe to the ics file. When you push changes to the ics file, they would automatically propagate on the calendar.

2. Use built-in org html export features to generate a simple page showing your schedule and either host it on your local network or put it in a shared directory as described above.

edit: sibling comment has a better suggestion (org-caldav)