To me omnipotence means that there is no single act that he is not capable of doing.
There are two significant factors in that definition:
1) It simply says that there is nothing he is not capable of doing, but does not imply that he ought to do any particular act. So he has the unlimited potential to do anything, while at the same time remaining selective in terms of how he uses that potential.
2) I define it as "a single act" because when we look at situations involving multiple variables there are conflicts and paradoxes that arise. Is God capable of both killing me eternally and keeping me alive eternally at the same time in a single universe? The fact that this is not possible for God does not in any way detract from his omnipotence. It's just that we are capable of phrasing paradoxical questions that are outside of the realm of reality.
So could God have remove the cup from Jesus? Yes, as a single act he was obviously capable of doing so. But if he was going to do that then probably he could have avoided a lot of time wasting by wiping out Adam and Eve at the outset and starting again. Just because he was fully capable of doing something different does not mean that he will do so if it is not the best action. To assume that it was the best action is to work on the premise that there is nothing more important than for a loving Father to keep his Son from pain. Clearly from God's perspective this is not the case. There may have been nothing more painful than to watch his Son suffer and die, but that is a different matter from what he decided was most important and the price he was prepared to pay (John 3:16)