This is Mapquest directions for the fastest, most direct route to drive from the old Dallas City Hall to Parkland Hospital.
So, you can see what direction they had to go, which was west. However, Oswald's ambulance exited Commerce, and turned left, which was east. So, it was going the wrong way. That was by necessity, since Commerce is a one-way street. But then again, it was an ambulance. Don't ambulances sometimes travel the wrong way on a one-way street, if necessary? It was an emergency.
However, it was a long ramp that went through from Commerce to Main. So, why didn't they instead go out the Main Street entrance, which would have allowed them to (legally) go west? Plus, they would not have had to wait for the Brinks truck to be removed from the Commerce Street entrance. Plus, Main was the right direction anyway.