James I had only 2 children who reached adulthood - Charles I and Elizabeth of Bohemia, both rulers. Of those only Charles had any offspring outside the royal family - perhaps quite a few! So it would be a bit surprising to be descended from Mary without being descended also from James and Charles.
I have never seen a whisper of Charles l (i.e. Charles first) having offspring outside of his marriage. Please do tell me more.
His son, Charles ll (second), was profligate of course, and if a family history could be traced back to one of Charles 2nd's bar sinister children, then that still goes back to Mary Queen of Scots.
I, too had an assumption of Charles 1 being abstemious. It may have been incorrect. He didn't marry until he was 25.
His elder brother, Henry died aged 18.
Another Prince Henry (1640-1660), Duke of Gloucester & Earl of Cambridge was youngest brother of Charles 2nd and James 2nd.
I don't know if either Henry had offspring. Henry, Duke of Gloucester spent his teenage years in exile in France. He did some soldiering. Who knows what else he got up to.
Henrietta, youngest daughter of Charles 1 married her French cousin, the Duke of Orleans. Descendants of one of their daughters were kings of Sardinia.
Elizabeth of Bohemia, daughter of James 1st was mother of Sophia of Hanover (mother of King George 1st of England), Princes Rupert and Maurice of the Rhine + 6 other children. Rupert and Maurice of the Rhine assisted their Uncle Charles in the English Civil War. I'm sure English Royalist women loved them.
George, Elector of Hanover was accompanied by his 2 favourite mistresses when he travelled to England to be crowned King George 1. KG3 had a lot of children with Queen Charlotte. Their sons had mistresses and morganatic marriages and lots of children.
Then there was jolly Edward Seventh, great-grandson of KG3. Isn't Camilla, Duchess of Cornwall a Stuart descendant and a distant cousin of Prince Charles, Diana and Sarah Ferguson? That's even without King Edward as her potential great-grandfather.
Potential multiple routes of descent from Mary QoS, many criss-crossing.