Equivalence in General Relativity

I have been reading Lisa Randall's book Warped Passages. She explains with extraordinary clarity. I knew that Einstein has based his ideas for Special Relativity on the idea that you cannot feel the difference between standing still and moving in a straight line at constant speed, These are the two conditions stipulated in Newton's First Law of Motion. I also knew about the equivalence between inertial and gravitational ,mass. But Lisa Randall made it very clear to me that General Relativity hinges on Newton's Second Law of Motion in a similar way to Special Relativity hinging on the First Law. The idea is that acceleration of a mass comes from a resultant force. Or put it this way: if the car accelerates very rapidly, you feel pinned back in your seat in a way equivalent to gravity pinning you to the ground, I knew this stuff but I hadn't made an explicit connection to an equivalence in the Second Law like that in the First Law with Special Relativity.