Add database to availibility group
It sounds like you are trying to add a database to your AG from a node other than the primary (is instance3 even part of your cluster), you can't do that.  You would have to fail over to instance3 and then add it.  You could also take a backup of your database, restore it to the primary, then go through the steps to add it again (you'll have to do a full backup and log backup from the primary).

Your biggest problem is going to be the name.  You are correct, you cannot have two databases with the same name.  It will have to change or you'll have to move it to a different cluster.