Impossible is not a nice word, so, to stick with your phrasing, yes, the idea is nuts. I assume that you are on holiday, not attending boot camp. Take a bit of time to enjoy things. In Andalusia schedules seldom go as smoothly as one might hope. The trick to life there is to learn to appreciate the tapa that you end up eating while waiting for the rental car to arrive, the people you meet while trying to find the entrance to the museum, etc. While in Cordoba, you really should check out the Moorish baths right around the corner from the mosque (You'll need to pack a bathing suit).