If this is just happening in recent, existing saves, are any of the characters encumbered? If so, in single player drop or transfer the excess weight, save and then see if you can play multiplayer.
Did you try older saves or a new game (create a new profile first, to keep the saves separate, and you don't have to worry about a test game overwriting quick or auto saves in your current game).
Did you try switching who was hosting? You can test in a new game, or transfer your latest save to the other person. Each save is a folder in the '..\Documents\Larian Studios\Divinity Original Sin Enhanced Edition\PlayerProfiles\<ProfileName>\Savegames_patch' folder.
