Yes, in Spain, Infanta Amalia and Infanta Paz were always styled HRH Infanta. But letters sent by King Alfonso XIII to her aunt, for example, were sent to IKH Prinzessin Ludwig Ferdinand von Bayern.
This was something that royal women frequently found themselves in, since princesses have traditionally been expected to leave their native lands and marry foreign royals. As long as a marriage was dynastic, a wife could expect to be styled by her husband's title and qualifying rank.
Has it generally been the practice, then, that if the husband's title and qualifying rank were higher, then she simply ceased to use her birth title (with qualifier) altogether -- even when paying return visits to her native land? Case in point: HIH Grand Duchess Olga Constantinovna of Russia, granddaughter of Czar Nicholas I. At marriage, she automatically became HM Queen Olga of the Hellenes, since her husband was the already enthroned King George I. I'm assuming, then, that she had no reason to ever again style herself with her maiden title with qualifier. That even during her frequent trips to Russia, she was known only by her elevated title and rank -- correct? Of course, one might see something like the following: "Her Majesty Queen Olga of the Hellenes, née Her Imperial Highness, Grand Duchess Olga Constantinovna of Russia."
If, however, a woman's title and rank at marriage were roughly comparable to those she enjoyed at birth, did she simply style herself with multiple titles?
The four daughters-in-law of King Ludwig I of Bavaria, for instance, were all born with different maiden titles (i.e. Princess, Duchess, Archduchess, and Infanta). The first two both became queens, and hence were in the same situation as Olga of the Hellenes.
But the third was an Habsburg born to the imperial rank, who married a Wittelsbach born to only the royal rank. Was she styled, then, as "Her Imperial and Royal Highness Princess Luitpold of Bavaria, née Archduchess Augusta Ferdinand of Austria, Princess of Tuscany"? Or did she perhaps simplify matters by calling herself one thing in her native land (i.e. HI & RH Archduchess Augusta of Austria, Princess of Tuscany) and something else in her adopted land (i.e. HI & RH Princess Luitpold of Bavaria)? I believe that a wife born to a higher qualifying rank has generally been allowed to retain the said higher qualifier (e.g. Imperial Highness), and either drop the lower one (e.g. Royal Highness) or use it as a second qualifier.
In Great Britain, however, Queen Victoria insisted that her second daughter-in-law, the Duchess of Edinburgh, style herself ROYAL first, Imperial second: when in Rome, do as Romans do. Things were certainly different in Germany, where there was great respect for a wife's birth status. Archduchess Gisela of Austria (daughter of Emperor Franz Joseph) was allowed to style herself Imperial first and Royal second, as a princess of Bavaria after marriage to Prince Leopold (second son of Prince Luitpold).
What about Infanta Amalia of Spain, wife of King Ludwig I's youngest son? Like Princess Marie of Prussia, she was a king's granddaughter and a Royal Highness by birth, who married a fellow Royal Highness (a king's son). It's just that her maiden and married titles were different. Did she simply call herself Infanta Amalia in Spain and Princess Adalbert in Bavaria?