Nylons or not, she "put on new stockings just to please" Casey. Two other passages refer even more directly to a physical/erotic attitude: "just a kiss to make a body smile" and "Still, she said, it's so blessed good to feel your body". If it is the mother, she is either demented or incestuous, by English standards.

The strongest argument in favour of the mother theory is the line "now that you've a family of your own", suggesting that formerly both were members of the same family (could be brother and sister, though).

Whatever the relation, Casey is not pleased, but more depressed than before. The family of his own is in fact no longer in function, probably by divorce, without the lady's knowledge, and probably without Casey informing her of her error (as he would have done if he considered reviving an old friendship).

The song being so well-known for a long time, KK must have been asked about its meaning. I guess his answers will one day surface to the Internet, if it has not already.