According to her Wikipedia article Frederica's husband Gustav IV Adolf was the last Vasa King of Sweden. They were exiled and moved to Baden. She was impressed by relatively relaxed morés in the Swedish court. She was the daughter of Amalie von Hesse-Darmstadt. Frederica's older sister Elizabeth landed a Tsar for a husband, not just a mere King.

ca. 1800 Frederika Dorotea Vilhelmina of Baden and King Gustav IV Adolf of Sweden by K. G. Pilo or Jonas Forsslund (Gripsholms slott - Mariefred, Södermanland, Sweden)
