Thanks for the question, Anon.
The first Targaryen prince to consider is Maegor, who wed (twice) before he became the usurping Lord of the Seven Kingdoms. Yandel refers to his first wife as “Lady Ceryse of House Hightower” when noting that Maegor was wed to the High Septon’s own niece in 25 AC. After that, Yandel only calls her “Ceryse”, not even “Queen Ceryse”, though she did nominally become queen when Maegor ascended the throne in 42 AC (as she only died in 45 AC). Maegor also wed before his accession the Lady Alys Harroway, and she, unlike Ceryse, did get the title of Queen when Maegor proclaimed himself king: Yandel refers to her as “Alys”, “Alys of House Harroway”, and “Queen Alys”. So, it appears that - to the extent we can speculate - Maegor’s wives were only called “ladies”, not “princesses”.
The next case to look at is Prince Aemon Targaryen, eldest surviving son of King Jaehaerys I and Queen Alysanne. He married his half-aunt, Jocelyn Baratheon, and together they had one child, Princess Rhaenys, the so-called “Queen Who Never Was”. Yandel calls her “the Lady Jocelyn”, while Gyldayn refers to Rhaenys as the “beloved daughter of Lady Jocelyn Baratheon and Prince Aemon Targaryen”. Their notes seem to imply that, at least in the historical sources to which they refer, Jocelyn was only ever called a “lady”, not raised to the status of princess. One might expect that, as wife of the Prince of Dragonstone, Jocelyn might have been herself called “Princess of Dragonstone” or “crown princess”, but this is never a style in the books granted to the wife of the heir: only Rhaenyra and Daenerys are thought of with the former title.
Alyssa Targaryen was also wed to a Targaryen prince - her brother Baelon - but hers is a less-useful case, as she was a born princess; Yandel only calls her “Princess Alyssa”. It is a similar story with Helaena Targaryen, wed to her brother Aegon during the reign of their father Viserys: she is in the histories “Helaena”, “Princess Helaena”, or - after her father’s death and ehr own coronation with her husband - “Queen Helaena”.
After the Dance, Viserys Targaryen - the future Viserys II - was wed to Larra Rogare, the daughter of one of Lys’ greatest banking families. Larra never ruled by her husband’s side - fleeing him and their children to return to Lys in 140 AC and died in 145 AC, over 25 years before her husband became king - but for the time she spent at court, as wife to the heir, Yandel refers to her only as “Lady Larra” or “the Lady Larra Rogare”.
Maybe interestingly - or maybe I’m reading far too into it - Yandel gives no title to Naerys Targaryen (other than “Queen” when Aegon ascended the throne). Although she was married to Aegon for nearly two decades before she became queen, Yandel only ever calls her simply “Naerys” (even though he calls her unworthy husband “Prince of Dragonstone”). Even Daena, though largely referred to only as “Daena”, is at least twice called “Princess Daena”.
Unfortunately, we don’t get any view into the address of the wives of Daeron II’s sons (although Septon Sefton calls Aerys’ wife “Queen Aelinor” during her husband’s reign): Yandel only once refers to any of them - saying that Aerys I had been “wed to Aelinor Penrose” but that he “never showed an interest in getting her with child” - and we only know their identities thanks to the helpful Targaryen lineage in TWOIAF. Based on the Jocelyn Baratheon example, I presume at court they were called “Lady/the Lady Jena/Aelinor/Alys/Dyanna”, or “Lady Jena Dondarrion/Lady Aelinor Penrose/Lady Alys Arryn/Lady Dyanna Dayne”; perhaps the women were also more formally introduced at times as “the Lady Jena of House Dondarrion/Aelinor of House Penrose/Alys of House Arryn/Dyanna of House Dayne”, the way Sansa was introduced when she begged for her father’s life before her betrothed Joffrey.
It’s a similar story for Maekar’s sons. We know that Daeron married his cousin’s widow, Kiera of Tyrosh, and Aerion his cousin Daenora Targaryen. For the former, I presume she was called “Lady Kiera” or “Lady Kiera of Tyrosh”; the latter, as a born princess, needed no other state, as Alyssa and Helaena demonstrated. Aegon, of course, wed Betha Blackwood - called “Lady Betha of House Blackwood” formally by Yandel, and then after that by her much more informal nickname, “Black Betha”. We’ll almost certainly get a better handle on how Betha, and perhaps Aegon’s sisters-in-law as well, were addressed in future D&E tales.
Now, as for the daughters of Daemon and Laena, it’s actually interesting.
Baela is called “Lady Baela” when referred to as the rider of the dragon Moondancer, yet she and her sister Rhaena are also called “princesses” when they present Daenaera Velaryon to Aegon III.
The Queen Regent (NFriel)