In my opinion, when the man sings the words "laid her in the shade" he is continuing his lament that he was good to his woman since he made life easy for her by providing a hammock or lawn chair [or red rocking chair, though I think that might have been a reference to an indoor piece of furniture} on which she could lay down in the shade and relax.

Since that man "works every day" but his "sugar baby" [sweetheart] "throws it all away", he is tellin her that he's gonna send her back home to her folks.

As to the words "rock that cradle when you're gone"-I'm wondering if these words refer to an actual cradle? Is he saying that he's gonna keep the baby {who sleeps in the cradle} or is he at least threatening to do so?