So to sum, you have a broken cluster and cannot repair with bringing the third node online. Fixing this is possible but could be painful and with much potential downtime. What I'd recommend depends highly on how much available cluster space you have, and what type of storage you're using. Do verify that you dont have network problems, esp on the corosync interface.
IF you have clustered storage, migrate all your assets to one of the surviving nodes and evict the misbehaving node.
IF you do not have clustered storage, you'd need to migrate assets manually offline to either of the survivor nodes, either with zfs send if available to you or vzdump.
Once you do that, reinstall proxmox on the broken node MAKING SURE TO GIVE IT A NEW NAME, readd to the cluster and away you go.