A few points . . .
In 1922 Dicky was
Lord Louis Francis Albert Victor Nicholas Mountbatten. His and Maria's children would be Mr and Mrs Mountbatten until he was ennobled and then the younger sons would be the Honourable <firstnames> Mountbatten. The daughters would still be Lady <firstnames> Mountbatten. Presumably Dicky would be ennobled because of his connections to the Royal Family, though I doubt it would be "Mountbatten of Burma". Still, he would do well as the receiver in bankruptcy of the Raj. Imagine, a Russian Grand Duchess being the Vicereine!
Whatever has Tatiana done to be the daughter-in-law of my cousin
Nancy Astor?
It's Princess Royal, not "Princess Royale" unless Jules and Vincent are ordering a BarbieBurger from McDonald's in France.
Besides,
Mary lived until 1965 and the title was for life, so David's and Olga's daughter couldn't become Princess Royal until then.
And, just who did they say
Fraulein Unbekannt, the woman fished out of the
Landwehrkanal in 1920, was?