It is not mentioned clearly that he is betrayed by his own family, but rather by a future king of Lucis not yet chosen by the Crystal, which is a quite weird statement as we know only Ardyn and then Noctis were Chosen Kings... Not "yet" could mean that he was chosen after that or that he wasn't chosen at all...
Noctis seemed to understand that Ardyn did what he did not just out of hatred, vengeance and such. When Ardyn was on the ground, defeated, in the Citadel, Noctis says to him "This time... you can rest in peace.", which sounded so heartfelt that it made me question their behaviour - Ardyn sounded peaceful and smiled peacefully too, like knowing one more step is done, while Noctis didn't treat him as a villain, but rather as ... another actor that needed to fullfil his role to the end, like Noctis knew the core of the problems are not all evil, but also there is a greater good pursued by both... yes, by Ardyn too. And I am not talking only a personal goal of finding the cure for his torturous immortality (the cure = being defeated and struck down by someone powerful enough to erase him from the physical world, and then from the astral world/after life dimension too, so that he wouldn't have the possibility to come back. I assume each time Ardyn would normally physically die, like when Shiva gave him her freezing kiss, he would spend time in the astral dimension, then come back as he's exiled from it forever, thus not allowing him to just die and rest his soul there). So I can see these goals:
♣ curing his immortality and curse (this is for himself and his own peace);
♣ ending the lines of Kings and Oracles, Lucis kings and Tenebraen oracles that is (as an eventual vendetta for the king that betrayed him but isn't that too little of a reason to act like he did for millenias? I think it is too little, so, in other lines, ending the lines of kings and oracles also results in disconnecting mankind from the Gods and their magical powers completely. There is no king to wield magic and magical weapons or to allow others to use it and there is no oracle to communicate with the gods to ask for their help, magic, power, aid, cure, previsions, anything. Mankind is now disconnected and alone unless the gods will decide to communicate with mankind based on their own godly will. So this is for ending an important link that granted huge powers);
♣ leading and even training Noctis often the hard way into becoming more and more the Chosen King, destined King of Light, with the power to end the curse of gods and bring back the dawn (now tis is where things get deeper, as I read theories about Eos, Ifrit, Pitioss, Ardyn and the Scarscourge, and it all makes me think that Ardyn in fact cleansed a great sin that the goddess Eos made, and he did so by planning out the complete erase of... her children and "users" of her power, which were the kings, the oracles, and Ardyn himself. If I may, I found this and this video (but there are more narrated by this youtuber that go deeper on certain aspects and I honestly would recommend watching them even if they're long, they present quite interesting points) that basically present this theory and more, except for the "cleansed Eos's greatest sin which got her banished" part, which is my thought after hearing and reading all the stuff.)
♣ was there a point which said that Ardyn wanted vengeance on the gods? But he must know well that even an immortal man is still a man and no god, so I think the way vengeance against the gods would be achieved is only through going out of their way, undo what they did, so - undo the immortality curse and undo the connection with mankind through kings and oracles. In no way did he want to erase all gods from existence or kill them, he gave the knowledge to kill a god to the Empire (aaaand the empire killed Shiva indeed) but he did not proceed to lead the Empire towards killing other gods for some reason...
Ah, well, my enthusiasm shows xD Ardyn always seemed off to me, I didn't suspect him to the the main villain and final boss not.a.single.second, can you believe that? I really thought Iedolas would be the main villain UNTIL the late, late, late chapters, so Ardyn managed to fool me somehow and that never happened to me before, I saw who's villain and who's hero in games with clarity always till now... Ardyn always seemed somehow sad, and somehow good-hearted, like... good-hearted-gone-wrong and... was he really all that corrupt I wonder? what does it mean he became corrupt after absorbing daemons (for the good purpose of healing people)? Because until the king betrayed and demonized him (again, now what does "betrayed him" and "demonized him" mean truly?), well, until that moment he, even with daemons absorbed, was considered a healer and loved by people. I wonder of what grave nature that betrayal could have been to turn him really from an angel-saviour figure of sorts to an assume-dangerous villain figure...