Is it correct to say "Don't YOU cry" instead of "Don't cry". I mean that I know that usually people you the second form (don't cry) but my question if there are cases that the first form (Don't YOU cry) is correct.
Yes, it is correct. The imperative does not usually have a subject, but we can use a noun or a pronoun to make it clear who we are speaking to. "You" is emphatic in this case.
- You take your hands off me!
- Don't you believe it!