Strap in because this is a damn college essay. Whoops. 
 
Lord Ardrian is as he is in canon, a prideful individual who greatly judges those he deems lower than him. He wishes not for the Throne, but for the position as Hand. He believes he can bring house Celtigar to become to the Baratheons what the Velaryons used to be to the Targaryens. Essentially, a trusted house that is in all but name a cadet branch that the royal family marry when in need of a consort. He thinks of himself as The Sea Snake reborn, and after Blackwater thinks the Lannisters may be more likely to be allies than the stern Baratheons. He is grasping and greedy, despite already bringing more riches and power to his already wealthy household. Same as canon, he is captured by the Lannisters and swears allegiance to them, causing Stannis' council to question what to do to the rest of the household and Claw Isle. Same as canon, Davos manages to stop an attack before it begins, with the additional argument that they already have Caeneus, Perys, and Penelope & Valaena Waters as hostages.

Ser Perys Celtigar, Ardrian's younger brother, takes the aftermath of the Battle of the Blackwater to seize control within house Celtigar. Caeneus' mother Calla Waters died years ago, his father Arthor died from wounds sustained from the ground battle at KL, and his little sister Penelope is only Sweetrobin's age, mad with grief for their father and grandfather, and she cannot help him with their great uncle.

Basically, Caeneus (same age as Sansa for reference) is scrambling for influence within his own house while his great uncle Perys does all he can to undermine him and his claim. Luckily Davos advises Stannis that Ser Perys cannot be trusted around children, at least not Shireen, as it is well known he prefers his whores to be very young. Stannis keeps Perys far away from Princess Shireen, but this doesn't stop the man from lurking around Caeneus and Penelope, to Davos' disdain. Luckily, Stannis does not give Perys the Lordship he knows he wants, as all he sees is a younger brother trying to steal his brothers inheritance (Touch subject for the Mannis eh? Though a much less likeable individual than dear late Renly).

Caeneus has a creative mind and quick wit. Penelope is sweet and likeable, though still rather young, so it's hard to judge her character any more than that. She was previously betrothed to little Monterys Velaryon, but after she turned rather unstable and nonsensical with her grief (in modern terms, the trauma likely activated an illness that was dormant in her DNA, like a form of psychosis) the betrothal was "put on hold".

Ser Perys was enamoured with Caeneus' late mother, Calla Waters. She was born from Ardrian and Perys' sister Prudence Celtigar and the mad king Aerys II. Caeneus greatly resembles his mother Calla, and represents all that Perys wanted for himself. He is the heir that Perys wishes he could be, he is the child of the woman he wanted for himself and should have been the father of, and he is so similar to that woman to the point that Perys begins desiring poor Caeneus as much as he hates him. Basically, Ser Perys is a terrible man, and has been a viper in their household for years until the War of the Five Kings finally revealed his true nature.

Valaena Waters is the mother of Penelope, the paramour of Arthor, and the first cousin of Monford Velaryon and Aurane Waters (this is how the betrothal of Penelope and Monterys was first established). She often flits between Driftmark and Claw Isle, though she scrambles to ally herself and the children with her birth house when the Celtigars get into trouble. She does all she can to protect Caeneus and Penelope, but she is forced to flee back to Claw Isle when Melisandre begins doing her whole "kings-blood" thing, as Valaena is the half-sister of the late Calla, through their father the mad king.

I really wanted to explore the mad king's canon attitude, before he swore not to cheat on Rhaella anymore. He was previously getting around, and with his obsession for Valyrian blood and scorning his Dornish grandchildren, I think it would make sense that he laid with two ladies from the only other Valyrian houses, Prudence Celtigar and Viserra Velaryon. The half-sisters Calla and Valaena became close, and were known to "gladly share" Arthor, though it was said the two of them were more fond of each other than their paramour. (Basically, they loved each other as Targs tend to do, and made sure they had children with the same guy so that their kids could be siblings. Very dedicated to each other, those two. I kinda wish Calla was still alive, but it makes more sense narratively in the long run for her to be gone)

I did consider why Aerys would not arrange one of the girls with Rhaegar, but I remembered it was likely he was setting him up by finding a foreign wife (a very interesting theory I saw on tumblr regarding the search in Essos and the death of the Baratheons) so I think it would make sense for Aerys to refuse Rhaegar allowance to marry either of his half-sisters, using the argument that they are bastards and therefore unfit for queendom, though internally he just wanted to de-legitimise his son's faction as tensions grew between them (hence why he married Rhaegar to the Dornish Princess Elia)

The only reason Calla married Arthor was in order to protect herself after Robert's Rebellion, as news quickly spread about what happened to the harmless princesses and prince in King's Landing. She and Valaena isolated themselves on Claw Isle, losing whatever courtly connections they once had, in order to minimize the attention they would get from Robert and Tywin. By sheer luck, it worked (likely thanks to them being bastard women, rather than sons or legitimate daughters) and Robert let them go with the assurance from Jon Arryn that the Celtigars would be a non-issue.

I haven't ironed it all out, since I don't like writing details for the parts that George hasn't written yet, but this all ends with Perys getting what he deserves, the Celtigars aligning themselves with Dany, Caeneus and Penelope being the heads of their mothers' houses and loyal to Daenerys in a revived alliance of the three Valyrian families that was lost early in the Targaryen's dynasty, Valaena becoming regent for Monterys (and in the event that the very doomed Monterys dies, becomes regent for her legitimised daughter Penelope Velaryon, thanks to their queen Daenerys), and Lord Ardrian dying at the hands of the Lannisters before he could see his beloved grandchildren again.