I think I have a way to balance the nukes:

First of all, regardless of how the fantasy nations enter our world, they're probably going to end up in a country that doesn't belong to them, regardless of whether it's one "portal" several "portals" or a sort of overlap of the worlds. So, nuking a magical nation you don't like that's sitting in or near a country that either plays an important role in your nation's economy or would kill millions of innocents wouldn't necessarily be an easy option.

Then, the alternative. Let's say you're India, and France is really pissed you off by taking a magical, rare resource you wanted. Sure, you could nuke them. But they have that resource you want, and destroying France could destroy most, if not all of that resource. Not to mention all of the innocent dwarves and elves that may be living in or around France.

So, saying "we'll nuke you if you don't..." is going to be different, because you're threatening a countless number of innocent people that happened to be teleported there or happened to have people teleported there. Not to mention all the repercussions of nuking a country that's your ally just to get the magical guys inside of it. At that point, it's not MAD. Because after you fire those nukes, every single country in the world is your enemy. So, instead of all of the countries blowing up, it would likely just be two.