@Abetillo Poseidon at first felt jealous, lonely and overlooked by his older brother, like Hades "replaced" him with Twilight. In reality, that's an issue in the relationship between Poseidon and his older brother, not the relationship between Poseidon and Twilight—which is why he acknowledges that Twilight hasn't done anything wrong,
but because of that unresolved tension, Poseidon still feels like he's an intruder and unfairly resents him a little. Although Poseidon would be able to join them as part of the group and wouldn't be left out in that respect if he lets his dislike go and gets along with Twilight, it wouldn't address the hurt in his original one-on-one sibling relationship with Hades
and the problem would be solved in everyone else's eyes. He doesn't really want to get along with Twilight while he still kind of resents him and feels lonely, since that would mean his brother, who hurt his feelings, and the intruder, who he resents a little, would "win." (Petty, but people tend to have trouble letting go of relationship tension if the other party/parties are wholly oblivious.) Note how he doesn't want his brother to feel happy about Twilight getting more emotional support, because that would mean he'd be thinking about Twilight's happiness while Poseidon is having reservations, again, rubbing salt in the wound if he does decide to set aside his feelings of hurt and play nice so they can all get along.
The most direct solution is for Poseidon to tell Hades how he felt so he can move on, but if he can let go of his old feelings through other means, that'll work, too. Maybe they could talk shit about Hades together, that's a time-honored younger sibling bonding activity.