I have what is essentially a shopping cart that needs to have two separate checkout options. The first of which takes the user away from the site, but form data must be post
you could set an onclick handler to the buttons and change the form action dinamically.
I'm giving this answer because you have the javascript tag and i assume the external site receives the parameters via POST METHOD so you could not make a redirection in php
But i wouldn't trust in this because it require the users having javascript enabled...