In the UK, nylon stockings are usually called "stockings" not nylons. As in our love of ladies in "stockings and suspenders" which would probably be called "nylons and garter belt" in the US. We NEVER call women's stockings socks, and we don't call socks stockings either except for those that come to just below the knee. I am NOT elderly, but I am English.
A lady wearing stockings instead of tights (pantyhose in the US) would be a very good way to get a man excited.
Unless Casey had a very peculiar relationship with his mother, this song is about a man remembering the last woman he made love to. He would find it difficult to be turned on by his wife afterwards as he would always be comparing her to this much sexier girl and this would adversely affect his marriage.
The reference to "a family of your own" may well be because the woman is a married woman with a family who has had an affair with Casey, which would go a long way to explain why he cannot be with her and why she is willing to see him in the first place.