[...] And while Robert had been riding north to Winterfell, Stannis had removed himself to Dragonstone, the Targaryen island fastness he had conquered in his brother's name. He had given no word as to when he might return. [...] Pycelle had sent a raven off across the water, with a polite letter from Ned requesting Lord Stannis to return to his seat on the small council. As yet, there had been no reply[...] -Eddard VI & VIII, aGoT
[Stannis, to Maester Cressen:] "Why should I avenge Eddard Stark? The man was nothing to me. Oh, Robert loved him, to be sure. Loved him as a brother, how often did I hear that? I was his brother, not Ned Stark, but you would never have known it by the way he treated me. [...] I sat on his council for fifteen years, helping Jon Arryn rule his realm while Robert drank and whored, but when Jon died, did my brother name me his Hand? No, he went galloping off to his dear friend Ned Stark, and offered him the honor. And small good it did either of them." -Prologue (Cressen), aCoK
[Stannis, to Catelyn:] "[...] Lord Eddard did his duty, I will not deny it. Did I ever do less? I should have been Robert's Hand."
[Catelyn:]“That was your brother’s will. Ned never wanted it.”
[Stannis:]“Yet he took it. That which should have been mine. Still, I give you my word, you shall have justice for his murder.”
-Catelyn III, aSoS
[Dunk, to Egg:] "When the king named Lord Bloodraven his Hand, your lord father refused to be part of his council and departed King's Landing for his own seat," he reminded Egg. "He has been at Summerhall for a year, and half of another. What do you call that, if not sulking?"
"I call it being wroth," Egg declared loftily. "His Grace should have made my father Hand. He's his brother, and the finest battle commander in the realm since Uncle Baelor died. [...]" -The Sworn Sword
with all of the talk of what stannis and maekar had in common as kinslayers who nonetheless loved the victims of their respective fratricides, let us not forget these prickly kings' even stronger similarity: being so resentful over an elder brother denying them the title of king's hand that each ran away from the small council in king's landing, where they had loyally served their family for years, to go brood and sullenly sulk in their respective targaryen-built seats.
from that i wonder if we can extrapolate about the kingly brother and the hand chosen in maekar's place during that earlier era. not that aerys i and bloodraven match up to robert and ned's characters personality-wise, but aerys i could well have thought of brynden as his best friend and even the brother he chose. after all, bloodraven was technically their uncle, but like most of the younger siblings of daeron ii (including princess daenerys and all the other great bastards), he was closer in age to the sons of daeron ii than to royal big brother himself. brynden rivers was born in 175 ac, while aerys i would have been born sometime from 172-177 ac, meaning he was at most 2 years younger or even 3 years older than the uncle he chose as his hand of the king. with a common interest in the arcane, those two could have been quite close from childhood, studying old sorcery scrolls while baelor, maekar, and the other male great bastards spent more time studying the blade. with a relationship like that, bloodraven may not have needed to do any cunning politicking to get that handship position after the deaths of baelor breakspear and daeron ii. (after all, he could have been well content to just remain a spymaster as it seems most of his time and talents were taken up with the magical surveillance state anyway.) maekar may have naturally expected to become king's hand when baelor became king, as they had long worked as a team. and indeed he may have assumed his accidental killing of baelor unfairly lost him the chance at handship, but that doesn't mean it was true any more than robert ever intentionally slighted stannis with his denials. if maekar and aerys i weren't close the way he and baelor were (and there's no evidence they were), it's likely enough that he was never going to be hand to aerys i no matter how baelor died. the king just chose his own friend from a shared childhood over a brother by blood for the sake of common interest as well as trust, and maekar, like stannis, still felt that the position was his due as an ever-dutiful younger brother, never mind the personal realtionship he did or didn't have with the surviving brother he'd have to work closely with day-by-day. brotherly blood and successful battle command outweighed all else in the views of maekar and stannis, and if they couldn't have what they felt owed in recompense for their duty that only meant it was time to go back home, all or nothing.
but if stannis and ned could have been strong allies had ned not died for the sake of stannis's claim before stannis even acted, i think maekar and bloodraven could have had even more common ground in the end. even in the mystery knight, where war was predicted between them, that was only heard from those slandering maekar. more objective accounts emphasize the rift between maekar and king aerys i over the handship, as stannis's true beef was with robert. not only were brynden and maekar kinslayers defined by their fratricides and facing inaccurate suggestions of further kinslaying, (both being seen as capable of murdering rhaegel and his children to seize the throne, though maekar only killed baelor by accident and bloodraven only killed blackfyres on the redgrass field in service of his legit royal kin), they were also both known as stern and harsh wrt treason. which is why i think the 3rd blackfyre rebellion was what brought them together, as something must have for bloodraven to continue as hand during maekar's reign. the 2nd blackfyre rebellion was over quickly before it began with just bloodraven in charge and only egg acting in maekar's name, but the 3rd rebellion would be the first true blackfyre war since the redgrass field, with prince maekar and the king's hand leading the royalist forces together as baelor and all the other generals from the 1st rebellion were gone. when bittersteel was taken prisoner and king aerys i allowed him to try to go to the wall against bloodraven's counsel, instead of being executed for treason, i bet maekar agreed with bloodraven about what a mistake that was, the first time we know of aerys i disregarding brynden. (proof imo that he was not just a puppet under bloodraven's control)
this would then explain how maekar became heir to the throne, passing over rhaegel's youngest child, even though her elder sister had been named princess of dragonstone. if daenora's omission from tmk (where only the twins aelor/aelora were mentioned as rhaegel's children) means she wasn't born yet by the time of the 2nd blackfyre rebellion, that suggests a significant age gap between those princesses. naming an heiress 100 yrs after rhaenyra (when her granddaughters by aegon iii were already passed over) could already be seen as pushing it for a hand seen as sinister power behind the throne, whether the choice was truly his or the king's, but the idea of bloodraven serving a queen still a child would look too much like a power grab using a hollow puppet. aelora's death likely came around the time of the 3rd blackfyre rebellion or shortly after (the death of king aerys i himself coming 2 years after the war, while prince aelor died 2 years before it), so to preserve his own position and prevent any new succession crisis (can't allow any weakness in court to be exploited as opportunity by the blackfyres!), bloodraven could arrange a reconcilation between the surviving royal brothers with the understanding he could continue as hand to maekar as king. maekar may not have been trying to claim the throne but neither would he turn it down for the sake of a young niece with the security of the realm at stake, just as stannis would insist on not wanting the throne for his own sake while determined to claim it for the sake of the fractured realm.