Andrew - I assume you're asking if William, Jr (Madeleine's son) remarried after his divorce?
Because her husband William remarried and had children by his second wife. According to ET, her name was Virginia Montez Conner and she was originally of Akron, Ohio.
I went to summer camp with his grandson from that marriage decades ago (not divulging any info on him - wouldn't be right). It has already been noted here on ET that William and Virginia had a grandson who was interested in the Titanic. This must be my summertime friend, who was very knowledgeable about the sinking. However, he's obviously not interested in being public about it because he's had ample opportunity by now.
After Madeleine ended her 2-year mourning period following the demise of her husband John Jacob Astor she married her childhood friend William Karl "Will" Dick. As per John Jacob's will, she forfeited her inheritance and relinquished the Astor Mansion to her step-son Vincent Astor. No worry though, as Will was President of National Sugar Refining Co. (later Jack Frost), founded by his grandfather William and Harry Osborne Havermeyer; he was also involved in several other firms.
My grandfather was the chauffeur for Will and Madeleine during this period. Although they had a weekend/vacation estate (Allen Winden) in Islip, I have not been able to identify their Manhattan address.
I found this: Mr. Dick Is Vice President of the Robert Chapman Company and the McKee Refrigerator Company and is connected with many other large corporations. He belongs to a family long identified with the sugar refining industry. A portion of his fortune, about $3,000,000, was inherited from his grandfather, William Dick, a pioneer sugar refiner of Williamsburg. The Dick town house is at 20 East Fifty-third Street, and they have a country place Allen Winden, at Islip, L. I at:MRS. J. J. ASTOR IS WED TO WM. K. DICK