Wow! Seems like half the globe claims descent from King Sobieski. I too was told we were direct descent. I grew up in Ireland and the connection is on my maternal grandmother's side ( Anglo-Saxon Protestant.)
What I have found is that John Sobieski's son James m. Eliz Amelia of Pfalz-Neuburg. Their daughter, Maria Casimire Clementine Sobieski (b.July18 1702 and d.1735 in Rome and is buried in the Vatican). Anyway she married James STUART, Duke of Cornwall and their son -Charles STUART, Prince of Wales, b.1720 wed Louise Maximilienne, Princess Stohlberg. HOWEVER there were NO CHILDREN, BUT the said same prince was "associated with" Clementine Walkinshaw, Countess Alberstroff and by her he had a daughter - Charlotte STUART, Countess of ALbany b. 1753. died 1789 .. I cannot find if she married / or had children. It would appear, at least in Engand and Ireland back then that the illegitimate children of royalty were given noble titles to compensate for their lack of legitimate claim to land/thrones. Anyone knowing anything further about Charlotte STUART, Countess of Albany.. I'd love to hear.