This rumor of Beatrice and Alfonso XIII has been ongoing for decades, but, again, without much proof, at least none that I have been privy to.
In 1909 when newspapers reported that Manuel II of Portugal was "courting" Beatrice, Alfonso de Orleans lost no time in arranging for his marriage to Beatrice, once he finished his studies at the Military Academy in Toledo.
King Alfonso XIII had expressed to his first cousin Alfonso de Orleans that he had no objections to the marriage. From Toledo Alfonso went to Coburg, where he and Beatrice married at the Rosenau, in a mixed Catholic-Protestant ceremony, with the cavet that their children, if any were had, would be raised as Catholics. Alfonso sent his cousin the King a telegram in which he said:
I have the pleasure of communicating to you that we have married civilly and in church. I leave for Paris on Tuesday. I hope you will allow me to serve our motherland and its King...
But the reaction of the King was the complete opposite to what was expected!
A telegram sent to all members of the Royal Family caustically read:
I have to announce to you, that the Infante Alfonso de Orleans, having contracted matrimony. without my pemission, with Princess Beatric eof Coburg, by decree dated today, he is exonerated from the dignity of Infante of Spain, and all the honors and prerrogatives pertaining to it. Alfonso
Arturo Beéche