Putting it together, "red rocking chair" makes most sense when meaning her vulva, the "juice" her sex fluids, with repeated "red" filling the musical void "no use for your ____apple juice". Squeeze a red apple you get sweet amber juice so the red might remind one of sex during a period.   I doubt the prostitute bit despite the "dime", because he threatens sending her back to her mamma next time he gets the money, wouldn't do so with a prostitute. "Dime" probably just refers to his bitterness of supporting her while she's abandoning him and their baby, since the words "sing the song" probably means a lullaby. Bitter, dark. Angry A men-only song, hard to understand covers by women singers. Bray-Cravens 1962 version might be the best in Em and G which give a proper creepy touch.