There is a command to move tab to other side.. you should be able to create a script so it first call the Dupicate Tab command then then Move to other side.
User Defined Command of type CustomCommand can run an internal command with the command "MC.Run ID=<command id>"
And the "Command ID" it is found in the Keyboard customization dialog under the "name tag", For example for the command "Move Tab - Move Active panel to other side" you will see that it has a the value "Core.1061" This is an internal reference to this command and can be used from CustomCommand scripts.
But Custom Commands can only run one command. And you want to run two.. (Dupe and move )
But the more advanced Multi-Script Can also run CustomCommands and can run multiple commands of them.
So.
Create a User Defined Command of "Multi-Script" type
and insert
MC.RunCmd ID=Core.1322
MC.RunCmd ID=Core.1061
Then save the command and then assign a hotkey/menu option for the command.