I think Gwendoline's maiden name is Coate.
You will find a marriage record (1898) at familysearch.org in Brooklyn NY for Andrew Kugel and Gwendoline Coate. Her parents are listed as Henry Coate and Margaretta Powers.
Gwendoline is in the 1900 census with her husband and daughter Henrietta and her parents and sisters Daisy Coate and Charlotte Coate.
If you go to fultonhistory.com you will find an article in 1909 about Gwendoline Kugel who married Milton Wike on his deathbed. The article states she was divorced from Andrew J. Kugel on September 15, 1908.
There are a few articles about Gwendoline and Charlotte Coate. It looks like they were involved in the theatre as actresses and singers.
You will also find the death records at familysearch.org for Gwendoline's father Henry G. Coate and her sister Daisy Jacobs. The records state they are both buried in Evergreen Cemetery. You could possibly call Evergreen to see if Karl and Gwendoline are buried there.
There is a marriage for Henrietta Kugel in 1921 in Manhattan to Joseph Gillette. Henrietta's parents are Andrew Kugel and Gwendoline Coate.
There is a birth announcement at fultonhistory.com for Gwendoline, daughter of Joseph and Henrietta Gillette.
Good luck in your search. Kathryn