Hi Telfer,
Have to say, you're really off on your understanding here (as a number of others have said). But to put it in the terms you are using here, here we go.
The law you are refering to is Newton's 3rd Law of Motion, the first dealing with inertia, and the second deals with application of force. Pretty important stuff for us to understand and get right. The third law is, as you said, that every action will have an equal and opposite reaction. Unfortunately, you are rather out in where you think that equal and opposite reaction is. And your "wall" experiment is just plain wrong, sorry.
If you strike, as you say, with one shoulder going forward (the striking side, let's say the right here), causing the opposite (the left) to go backwards, then you have lost half of your potential power backwards, and really need to improve your understanding of power generation. Instead, as you strike forward, the balancing force goes back down into the ground through your legs and feet (what most TMA guys and arts refer to as being "rooted" or "grounded"). As we teach it, the pivot point is not your spine, as that results in the aforementioned loss of power, but the opposite shoulder/hip. Think of your body not as a revolving door, but as a gate swinging on a hinge. That way all your body weight goes forward, there is no bouncing off of anything, and you get maximum power generation. And it follows Newton's Laws.
The trick is to prevent the reactive force from acting on anything but the target? Nope, you've kind of lost physics again there. From the sounds of things, you've got a little way to go, so I'd start paying attention to those trying to help you out, sound good?
As to your tricep acting as an explosive force, well, if you are really doing that you will have pretty much no power whatsoever. You are just using a fairly weak muscle in a rather inefficient way, and tensing it which reduces speed, and thereby power. Remember that 2nd Law? F = ma? Force (power in your strike) equals Mass (the weight of your strike, in your case just your arm, in mine my entire body weight) times Acceleration (the velocity or speed of the mass in motion, and by tensing your tricep to provide you with your "explosive power", you are slowing yourself down).
But back to the original topic. Double strikes exist in a number of forms, but the method you have described is rather limited, and not entirely powerful, but looks great in a WWE match. So I wouldn't expect to see it around.