We finally found some answers on the descendants of Robert Cade Taylor and his wife Laurence Taylor. Laurence took her daughters, Laurence and Mary Robert Taylor back to her mother's home in New Orleans. Laurence remarried briefly then divorced and died in 1929. Her daughters were raised by their grandmother and grandfather until his death in the late 1920's. Both the Taylor daughters (like their mother before them) were belles of New Orleans society, married in the 1940's and their children/grandchildren have been followed up into the 1970's/80's. The name Laurence continues to be a family name for each generation of girls.
It appears that Joseph Taylor may have died in January 1815. We have a Joseph Taylor of Hunterdon County NJ of the correct age, that enlisted in Baton Rouge 1813, in the Marine Corps and was assigned to the New Orleans detachment under Major Carmick. NJ War Records show that his death occurred during the Battle of New Orleans. No record yet on Anna.