What situations present them with a conundrum?
Legion spoilers below. Maybe. Idk. Legion rumors, at least.
A situation like Legion, really.
On the one hand, he hates the Burning Legion. Really, utterly hates it. So he’s 100% behind them getting their collective demonic asses handed to them yet again. If the Legion is finally cast away from Azeroth, from the universe, never to trouble them again? Great. Good. Let that happen. Less competition for him.
But he also really, utterly hates everyone on Azeroth. He is perfectly happy to watch Stormwind get set aflame again, to see Orgrimmar torn asunder. Let the Undercity echo with the screams of Sylvanas and her sycophants. Let Acherus fall from the sky; he’d just request a front row seat. Fordring’s death, possible corruption? Good. Let that son of a bitch suffer.
He’d probably try to not get involved at all, but eventually he might realize that the Legion has a bit of an upper hand here. They’re stronger than the Azerothians, more numerous, and fucking pissed. The situation for the home team might start looking a little dire, and at that point he might need to start considering whether he needs to get involved or not. Without the Lich King’s aid, Azeroth may be doomed. (Usually, he delights in irony. Right now, he wants to disembowel the whole concept.)
At that point, it comes down to a couple of things. First, who he hates most. That one he actually never quite satisfies, because he has a lot of hate, and the more he thinks on any of them, the more he hates them. So then he has to move on to less subjective considerations. Which side does he have a better chance of destroying after the war? The living, probably. He almost did it once, and if Tirion is dead then he’s in a hell of a better situation than he was in Wrath of the Lich King already. Who is less likely to betray him? The living. I mean, he expects that they will at some point, but the devastation will be of a smaller scale than whatever the Burning Legion can cook up.
So eventually, as much as he loathes it, he’d probably end up doing what Bolvar is doing in canon: Extending his aid against the Legion, powering up Mograine’s death knights to better slaughter the demons. There will, obviously, be a lot more animosity in this situation than in canon (not the least because Arthas’ return isn’t a well-known thing…), but when Space Satan is knocking at your door, sometimes the Lord of the Muderzombies looks slightly less worse than before.
TL;DR: Whenever he’s gotta take a side in a war between two factions he absolutely loathes.