Okay, regarding the Tempest Domain, actually gonna get into the nitty-gritty of realpolitik diplomatic relations here. Anyone who doesn't want to read complex political analysis of diplomacy between cartoon characters in an internet forum quest can just skip this post.
So, if we, Heinz Doofenschmirtz, Supreme Ruler of Doofania, reach out to the government of the United States of America offering to help broker a peace treaty between them and Drossel Juno Vierzehntes Heizregister Fürstin von Flügel, Duchess of the Tempest Domain, we benefit in the following ways: The Tempest Domain is a Sovereign Power within the territory that formerly belonged to the United States, just like Doofania. However, unlike Doofania, they lack the firepower to forcibly bring it back into the fold, and they know it. By getting the United States to recognize them as independent, it opens precedent for Doofania to be recognized as the same, particularly since, by offering to help broker a treaty between two sovereign powers, we implicate Doofania as being of equal standing to these two parties. If the US of A accepts this deal, it gives us a lot of legitimacy.
However, they can't afford to pass on it, because otherwise they get completely cut out of the communications between us and the Tempest Domain, and that could be disastrous for them. Worse, they can't even spy on our transmissions because they don't understand the language being spoken (and we should take care it remains so, leave any documents we keep of the Tempest Domain in their original language, not english). Also, by refusing the peace treaty, they might very well offend the Tempest Domain. So they need to come to the table, but that doesn't mean they have to take the deal as offered.
I can see them counter-offering to name us as a diplomatic envoy to the Tempest Domain. This lacks the strenght of them recognizing our status as a foreign power, but it still gives us legitimacy on our position in the Tri-State Area, as well as forging an unstable peace with the government: they can't come after us, because if they do the Tempest Domain could intervene in the name of "Doofanian freedom", which would be terrible for them politically, but we also sort-of compromise to not rock the boat too much or it'll force their hands anyways. Of course, during all of that time they'll be working around the clock to decipher the language we use to communicate with Drossel, and with us having already translated it it'd be considerably easier (possibly even within the government's ability) to decipher. However, the DEI headquarters physical and magical security is already insane, and as soon as our AIs come online on the cyberfront we'll be basically impregnable. That will pretty much start a race against the clock, and once enough time elapse either they'll continue trying to beat us or they'll resign themselves to working with us.
Besides, the current "heir apparent" of Doofania, Vanessa, wants nothing to do with all this nonsense and would like nothing better than to go back to normalcy, so the U.S. can probably afford to wait us out. However, if we recognize Norm and Princess Coffee Java as progeny, not to mention Genghis Khan technically being in the succession line, and the Tempest Domain also being ruled by immortal robots, the US might lose a little certainty on its idea of running out the clock on us.