I'm assuming that when you say "I have two MK2's", you mean, you have two players, and when you slide the second one into the same dock in your car, then the second player doesn't exhibit the bad behavior. (As opposed to, say, two MK2's installed in the car simultaneously).

When you say that it happens sometimes when the car turns a corner, that sounds like a loose wiring problem or a wire chafing problem. It's hard to tell from that if the problem is inside the player or if the problem is in the car wiring, because wire harnesses and connectors are involved in both places. If the problem is inside the player, it might even be as serious as a loose screw rattling around inside, or a frayed HDD cable or display cable. Or maybe a loose disk drive tray which is grounding out something inside the car when you go round a corner. Check for those things.

The fact that it happens to one player and not the other would indeed make it seem like the problem is confined to inside that particular player. But, not necessarily. It could still be an issue with the car or the wiring, and one of the two players is simply more sensitive to it than the other one. By any chance, is one of the players a MK2 and the other a MK2A? There are slight differences between the two with regard to how well they tolerate bad wiring, it's described here. If the MK2 is the bad one and the MK2A is the good one, then I'd still suspect a problem outside the player, such as loose wiring in the installation, or loose wires in the docking connector.