I can see your point moving to the left, however positioning the button on the right might well give the user a sense they are continuing along the process, as "next" buttons tend to be on the right hand side.
Considering that, I'd consider realigning your buttons to the right (where they obviously were before from your question wording) but utilise whitespace to the left to draw the user's eye.
As for button order, checkout should be right aligned. There's an excellent article at http://uxmovement.com/buttons/why-ok-buttons-in-dialog-boxes-work-best-on-the-right/ that makes many points for this, but the one I'm getting at here is:
When users click secondary action buttons, they expect the application to do nothing and take them back to their original screen. Thus, ‘Cancel’ buttons function like ‘Back’ buttons. When users click primary action buttons, they expect the application to do the action the button says, and take them forward to the next screen. Thus, ‘Ok’ buttons function like ‘Next’ buttons. Placing the secondary action button on the left and the primary action button on the right maps to the ‘Back’ and ‘Next’ button functions the user can expect.
It’s similar to how pagination buttons are placed. The button that takes users to the next page is on the right, and the button that takes users back to their earlier page is on the left. This button placement works because it maps to the user’s left-to-right reading and navigating direction, where right is the direction to progress and left is the direction to regress.
So we know we have checkout on the right. What about the others? Well, Continue shopping is more like a back button in this instance, so the most logical place to put it is on the right. This will also suit your UI if the button is styled as text and the others are styled as full buttons. That leaves us with the update button in the middle - also good for UX as if we were to, as the user will subconsciously, compare this to pagination the "middle" or "current" page will take us nowhere.