Since the moment the goddess pulled him away from the lethe, Hades had been entirely out of his element. There had been a definite clash. She'd made him angry, confused, and terribly lost. But now Hades wasn't lost. The goddess was presenting herself as an ally rather than an enemy. She was agreeing with him. He was agreeing with her. People did do irrational things to get rid of what they feared. Hades understood very well when she put it that way. The dog needed to stay. Not because Hades needed it to, or even wanted it to. The dog needed to stay because the new king of Olympus was reactionary. Hades wasn't sure what reactionary meant, but it sounded right.
“He's very reactionary,” Hades agreed. “Staying would be in the dog's best interest.” He spoke calmly and rationally, but maybe a little too quickly. When she said 'unusual', Hades wasn't sure if she was referring to the dog or the god. He knew it was probably meant to refer to the dog, but he decided that it referred to the god. Hades acknowledged that this was rather petty of himself, but denied culpability.
He paused as he considered the last part. “But I don't think the dog should be hidden. It doesn't matter if Olympus knows about the dog. They're completely severed realms,” Hades said. “Separate,” he amended. “If the Underworld wants to keep a three-headed dog around, that is none of Olympus's business or concern. The teeth aren't a bad thing. If anything, it's an asset that the dog has that many teeth, and is that big. If Olympus has a problem with a dog like that, I'd like to see Olympus get past it. If anything the dog should be displayed, so that they know the easiest way to not have to deal with the dog is to not go near that place.”
Hades paused. “I might have some idea where it is,” he said in reference to her request. Hades hadn't seen the dog lately, but it was a territorial sort. It mostly stuck around the Styx. He turned, and led the goddess the other way. She'd see what he was talking about best if he showed her anyway. As they were walking, Hades drifted a little further to the left to put a little bit more space between them. Since they'd started talking about the dog, Hades hadn't felt quite as out of his element. He feared that might be a warning sign that he was starting to enter her's.
He kept walking in the general area until a loud panting noise to the east beneath the sounds of the river told him they were close. Hades found the dog a few moments later, and stopped about ten feet away. It rested on the ground. Two of the heads were asleep, but the left was wide awake. Hades noted that this was another benefit to the dog. The left head looked up at them and tilted slightly. “This is the one,” Hades said in case that needed to be clarified. He still wasn't quite sure how unique it really was. Maybe she just hadn't seen a lot of dogs in the Underworld. When in a completely foreign territory, either everything was surprising, or nothing was. Hades mostly fell in the latter camp.