Since no one else has answered so far, may I start the discussion?
Your question greatly interested me, so I checked my books and am delighted to share the results.
1. Yes, you are correct: Some books say that there are two IMPERATIVES (commands). In your sentence, they are "go" and "take out."
a. In informal English, this is very common.
i. One book gives this sentence: Go and fetch some water.
(a) In American English, the "and" is often left out: Go fetch some water.
2. There is another explanation that is more difficult.
a. This explanation would analyze your sentence this way:
i. "Go" is the imperative (command).
ii. "Take out" is the PURPOSE. That is, it is WHY the speaker wanted you to GO.
(a) In other words, the sentence actually means "GO to take out the laundry."
Student or Learner