Alien administrations which acquire nuclear weapons are incredibly annoying to deal with, particularly if they come from absurd AI behavior rather than anything reasonable.
The TL;DR:
1) Eliminate the AA's special protection from coup d'etat if there are no alien warships in LEO or armies on the ground (excluding human armies controlled by the AA). It already gets huge advantages from penalizing opposing councilors running public campaigns, and having two factions (aliens and Servants) capable of running stabilize-nation.
2) Maybe consider having China use its nuclear barrages on invading aliens in preference to just ceding everything the moment Beijing gets conquered. I just think that maybe Chinese authorities would prefer to use their nuclear stockpile in obvious self-defense over just handing over the keys the moment Beijing is conquered.
On Alien Nuclear Weapons In General
The usual tools for sidestepping an opponent's nuclear arsenal are crackdown/purge and coup d'etat missions. The AA has special immunity to these missions. While technically you can pump unrest in the AA until it spontaneously coups itself, there are a few problems with that:
1) Public campaigns are very hard to run in the AA, with a -10 "Alien" modifier often combined with a censorship modifier for being totalitarian. Even when reduced to a single region, you need a high persuasion councilor to reliably pump public opinion, and +unrest is very hard to run unless you have either high public support or high command. At least with the coup d'etat mission, you only need one councilor to have a high command stat, but for pumping unrest, you basically need to sic your entire council on it for multiple turns.
2) It is much easier for the aliens and Servants to reduce unrest than it is for you to generate unrest, particularly if there's some undetected alien facility teleporting in a steady stream of fresh alien councilors to replace the dozen you've already killed. Sure, it locks up a lot of their councilor actions, but Servants+aliens outnumber your council 2:1 unless you can cut off the flow of aliens.
It then becomes a matter of either feeding armies facefirst into a nuclear meatgrinder or keeping your entire council in one region for months to years praying that eventually the aliens neglect to stabilize nation long enough for a coup d'etat.
The immunity to crackdown/purge makes sense as all the government officials are either aliens or closely controlled by the aliens. The immunity to coup d'etat missions, however, ought to be modified. If all alien/tripod armies are destroyed and there are no alien warships in LEO to bombard troop/protestor concentrations, the AA is basically just a few aliens at the head of a mostly human nation they're pretending to act in the best interests of. Particularly given the AA's allergy to ever putting pips in economy/knowledge/welfare, you'd think that lie gets threadbare awfully fast...
On Absurd Circumstances for Nuclear Weapon Acquisition
My past two games had the aliens land, very early (~2029) in an as-yet uncontrolled China and march to Beijing without any Chinese nuclear response. The first time it came out OK because they landed in Nanjing, and I was just barely able to wardec the AA in time and give the alien armies a dose of canned sunshine before they completed the move to Beijing.
The second time, they landed inland, crushed the Chinese army, and marched straight to Beijing, instantly capitulating all of China without even giving me a chance to respond. The entire US Army was prepositioned in Asia, but I couldn't wardec the AA until they reached the coast... and their first coastal province was Beijing.
It becomes the question of what China would do if alien armies were marching on Beijing.
1) Swallow their pride and ask the US for help.
2) Use nuclear weapons.
3) Keep on fighting from a temporary capital.
4) Watch the aliens roll into Beijing and immediately cede the entire country, nuclear arsenal included.
Somehow, I doubt it's #4, yet that is consistently what the AI does.
I don't mind it so much when the Servants get all Chinese CPs and peacefully cede China to the AA, but "enemy armies marching on the capital for the explicit purpose of conquest" is quite possibly the only situation most people would agree merits a nuclear response.
Nuclear-Armed Alien Administration Frustration
Re: Nuclear-Armed Alien Administration Frustration
Personally, I'd rather see terrestrial warfare reworked to having to occupy at least (Insert percent) provinces of the nation you are attacking rather than just having to land in a coastal capital with your armies. I'd reckon this is the devs still working out geopolitics to prevent some shenanigans before focusing on this so you can't blob up into a super-nation (Despite the fact that the Caliphate exists with claims on Indonesia, hello there Pavonis?)
In my opinion, any country with below 0 on the pro-alien sheet from Opinion should use nuclear force as soon as an alien army lands and starts occupation on their own teritorry, but not allies' (After all, those Salamanders are probably eating your citizens). This should go for factions controlling said nations as well.
However, this probably ties into that promised ground and sea warfare rework coming before full release, so dropping these is great.
In my opinion, any country with below 0 on the pro-alien sheet from Opinion should use nuclear force as soon as an alien army lands and starts occupation on their own teritorry, but not allies' (After all, those Salamanders are probably eating your citizens). This should go for factions controlling said nations as well.
However, this probably ties into that promised ground and sea warfare rework coming before full release, so dropping these is great.