There's a bit of debate about that one actually..
The marriage of Alex Boy's parents may not have been approved by the head of the Von Furtenberg House. If it wasn't approved, then the children of the marriage (alex and his sister) aren't Prince/Princess of Furstenberg. They also shouldn't be able to call themselves Von Furstenberg. (Von is a sign of nobility/royalty). Actually, in German his last name wouldn't even be Von Furstenberg. It'd be something like Prinzen Von Furstenberg or something along those lines. (See the Princess Caroline threads for her offical title as Princess of Hanover. It'll be similar).
However, I haven't seen anything regarding the marriage that says one way or another (the parents's marriage I mean) although the grandfather of Alex boy was not at the marriage of Alex boy's parents, leading me to believe that it wasn't approved.
So, she was probably not a princess during the marriage, and afterwards, more then likely did not keep the title (if Alex Boy had one).