Recently, as I reread Percy Jackson and the Lightning Thief (for the billionth time), something occurred to me. Percy Jackson is clearly banned from flying because of the rivalry between Zeus and Poseidon, so why are Jason, Thalia, Nico, and Hazel allowed to swim? Percy was threatened and nearly killed when he went into the Underworld and flew on an airplane, so why are the other children of "The Big Three" allowed to swim?
I think it is partly as in @Adamant's comment in that Poseidon is shown as a nicer god. Zeus is shown as immensely proud and quite quick to anger. This means he dislikes Percy Jackson flying as an infringement on his territory. Hades trying them was more that he thought they had taken the Helm of invisibility rather than Percy being Poseidon's son. Poseidon is shown in the books as a laid back and easy going guy which suggests he wouldn't just kill a demigod for entering the sea.
Secondly, I am not certain but I think Zeus got more laid back about the killing Poseidon's children thing after the Big Three prophecy was sorted. Before then Nico was safe in the Lotus Hotel or hanging out in the Labyrinth and the Underworld where he probably wouldn't be swimming. Thalia was either already bring hunted by Hades or a tree or Huntress for most of that time and probably wasn't swimming during the first two and protected by Artemis for the third. Jason we know was swimming as he killed a sea monster but the Romans seem less fussed by the Big Three prophecy also Jason was protected by Hera quite a lot. Hazel was dead at the time so unaffected.
Looking back on it, it does seem odd that Thalia, Jason, and Nico can swim in the sea. One reason may be that Poseidon is a more lenient god and doesn't mind it. But, in traditional mythology, Poseidon was aggravated more easily. But that still doesn't explain why Jason, Thalia, and Nico can swim but Percy cannot fly.
It is true that Poseidon is older than Zeus but the younger brother is the king of the gods and ruler of the universe. Therefore, Zeus can protect his children since he has power over Poseidon but Poseidon cannot easily do the same because Zeus is his superior in rank. It is shown that Zeus does like his two known children (Thalia and counterpart Jason). It is shown when Zeus kept Thalia from dying by turning her into a pine tree. I think why he couldn't just save her by making her human was because it'd be too obvious that he was favoring her and would upset the balance in Olympus and around camp. As for Jason, Zeus even says it himself:
"My son." Zeus clasped Jason's shoulder. "There is so much I would like to tell you..."
The god took a heavy breath, making the air crackle and Jason's new glasses fog up. "Alas as the king of the gods, I must not show favoritism to my children. When we return to the other Olympians, I will not be able to praise you as much as I would like or, give you as much credit as you deserve."
As for Hades, one answer might be that the Olympians are much too scared of him. They gave him the Underworld and no throne upon Olympus. This may be because of his dark aura and just how deadly he could be. Evidence shows when he captured Persephone, Zeus didn't hurry to help, his idea or not. But, it doesn't specify when/if Nico actually swims so, he is safe. Bianca and Hazel don't need to be too wary because, after the Last Olympian, the Big Three remains more calm about killing each others' children. Hazel, was dead and Bianca was in the Hunters of Artemis, protected by Lady Artemis one of the children Zeus favors, thus protecting Bianca.
As you can see, these are some possible reasons why Poseidon does not kill the other demigods when they cross into his territory.
Poseidon is generally a nicer guy than his brothers, Hades and Zeus. I mean, think about it.
"As for my brothers," Zeus said, "we are thankful"—he cleared his throat like the words were hard to get out—"erm, thankful for the aid of Hades."
The lord of the dead nodded. He had a smug look on his face, but I figure he'd earned the right. He patted his son Nico on the shoulders, and Nico looked happier than I'd ever seen him.
"And, of course," Zeus continued, though he looked like his pants were smoldering, "we must . . . um . . . thank Poseidon."
"I'm sorry, brother," Poseidon said. "What was that?"
"We must thank Poseidon," Zeus growled. "Without whom . . . it would've been difficult—"
"Difficult?" Poseidon asked innocently.
"Impossible," Zeus said. "Impossible to defeat Typhon."
Zeus seems a little less than eager to recognize his brothers as heroes.
He held out his arms and gave me a hug. I realized, a little embarrassed, that I'd never actually hugged my dad before. He was warm—like a regular human—and he smelled of a salty beach and fresh sea air.
Okay, okay, so Poseidon never hugged Percy before that, but at least he hugged his son, which Zeus did not. I mean, not his daughter. And Hades did not hug Nico. Does this give Poseidon some credit?
Do I even need evidence to convince you that Hades is not generally a very nice guy? Sure, Maria di Angelo, but I did mention generally.
So, yeah Poseidon tends to be nicer. I think it's the thing about water and blue and other stuff that Poseidon is that god of that we also attribute to calmness. I mean, the god of the dead and the god of lightning? That doesn't sound very...calm.
And after that very long list of evidence, we can draw the conclusion that Poseidon is the nice one out of the Big Three. So consequently, Poseidon would be one that is willing to let others into his domain without destroying them the second they enter (not that enemies will get a massage or anything).
It's because Zeus thought Poseidon took his master bolt. And the problem became worse when Poseidon claimed Percy, to which Zues theorise that poseidon sent percy to steal the bolt (because gods arent allowed to steal each other's weapons). And Hades also wanted to kil Percy because he too thought Percy was responsible for his weapon, the helmet of shadows or something (which was also missing). So basically any child of poseidon was thought to stole the weapons, and percy just happened to be the only one then.