OK here goes:
What I want to do is keep the programme Aperture on the computer a
For the Aperture program you do nothing of course it is already where you want it.
and have the photos on the external
OK here I need to confirm, you want to move the originals to the external but keep the library itself on the internal, correct? If so you would select all the images in your library and run File->Relocate Originals… from Aperture.
You will get a window that will let you select where you want the originals moved to (the external disk in your case) and how you want the folder structure that the originals will be put in to look.
with a backup (Vault) on the other external,
Once you have the library setup the way you want create a vault on the other external drive (File->Vault->Add Vault)and update it. Remember once the originals are referenced they will not be backed by the vault operation you will need to backup the originals using some other method.