I have the same family story. We were told that my great, great grandmother had two children by Franz Joseph (the children look exactly like him - a girl and then a boy) and then fled to the U.S. in 1896 with her children and a butler from the palace.
She later married the butler (his name was Albert Kitto). My Great, Great Grandmother's name was Franciska Konopaska. It is shocking to see so many families who posted to this forum with the same story. I am starting to believe we will never find out the whole story. Anyone have any suggestions how to find out more information?