I believe her official style is HRH Princess Beatrice, Mrs. Mapelli Mozzi. Edoardo’s father is an Italian count (by courtesy, since Italy became a republic,I think is the way it is put).

1. Does Pss Bea have her own coat of arms?

2. Regardless, the Mapelli Mozzis are armingers (see link). Could The Queen grant her the right to have arms of her husband impaled with her father’s?

3. I understand that the current practice is that the Court does not recognize foreign titles held by British subjects, with a few exceptions. (See e.g., the Gleichen’s, the foreign titles held by Dukes of Wellington.). Nonetheless, in theory HM could recognize Edoardo’s courtesy title so that Pss Bea (and her children) could be styled as HRH Princess Beatrice, Countess (or Nobile) Edoardo Mapelli-Mozzi. I would like to see her do that. If nothing else, it would be a nice work around her father.