If someone attacks my village, then, I click on the revenge button..I attack their village..will the clan that I did a revenge on be able to "attack" me again? Does this clan now have a "revenge" option?
No, you can only 'Revenge' on a normal attack.
Which means that if someone attacked you, and you Revenge attacked them, they cannot attack you back through Revenge. They won't have this option in their message box.
The only way for them to attack you back would be if they find you again on normal attacks, but that's rather unlikely since your trophy levels would now be different and there are so many players around the world.
Note that a clan member cannot Revenge for another of their members.