Help my car keeps shaking

[newbmwowner528i]

Hey, so I'm new to bmw, hence the username, I purchased a 2009 bmw 528i and haven't had much problems with it until recently. If I accelerate too hard my check engine light will come on and my car will shake however, if I pull over turn my car off and back on the check engine light turns off and the car drives like new..until I'm at a red light and my car rumbles and smooths out consistently. I've had the spark plugs, and the valve cover replaces today and it still does it. I'm assuming the rumbling is with the engine mounts, but that doesn't account for the engine light. The shaking and engine light only occurs when I hit the accelerator a little too hard, but not nearly all the way, I'm too worried about what would happen if I do that. I love this car and I'll probably stick with bmw for a long time but I can't seem to understand why it resets itself after I turn it off and on. Can y'all help me figure out what it could be?

Side note- the rumbling always happens when I'm idling. Doesn't matter if I had the engine light come on or not. The rpm's jump around 500 when it rumbles in sync with the rumbling.

[magamagapty]

While the car is on, unplug your coils one by one. If your idle rpm goes down, that coil is fine. If it the rpm does not go down, replace that one. Keep doing that until you hit the coil that is bad and replace it with another. I did that a few weeks ago and it worked like a charm.