Have you tried switching who was hosting?
Does this happen if you each create a new profile and start a new single player game?
Try verifying local files: in the Steam library, right click on the game and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Cache...' button.
With the GOG version, in the (optional) Galaxy client, select Divinity: Original Sin 2 in the left column, then click on the More button, and in the Manage menu select 'Verify / Repair'.
