"No" means "no." Someone more knowledgable in this can feel free to correct me on this, but notice that when it's more than one item it's "do no". I'm guessing the "no" in there would be the same "no" as the possession/"that one" marker. "Docchi no"serves the same purpose, but indicates only a choice between two items.
Aka no... = "the red one" Kawaii no... = "the cute one" Do no... = "Which one..." Ko no... = "This one..." Docchi no... = " Which one (of the two)..."
Nope Dono has NOTHING to do with AKA NO. DONO can not be separated into DO NO like you have done. It is one word. Just like we say HE instead of BOB or SHE instead of SALLY Japanese says AKA NO instead of AKA NO KURUMA all the time. This is covered quite well in course 1.
Luke, You have to have NO after DOCCHI because there is another noun after NO in the sentence. You cannot put two nouns side by side in Japanese sentences. Notice in DOCCHI NO PEN GA SUKI DESU KA? (= Which pen do you like?), both DOCCHI and PEN are nouns. You have to put NO after DOCCHI in order to make DOCCHI NO an adjective phrase to modify the following noun, PEN. Try to remember one of the functions of NO is a noun connecter.
By the way, DONO is already an adjective. That is why there is no NO after it.