I can't really see Padme as characterized staying with Anakin in this scenario or backing any sort of Imperial-like regime, whether it's led by Palpatine or Anakin, even for a regime that was significantly better than Sidious' empire was.
Padme at least in TCW was characterized by being an avid peacenik - to the point of opposing further mobilization during the Clone Wars, and seeking some sort of peaceful settlement with the Trade Federation / Separatists (which is basically insane, given how they were), and pretty much always in favor of the galactic senate and democracy as an institution, as well as being close with and politically aligned with the senators who started the rebellion.
IMO this... does not make any sense at all given who she associates with, the history of Naboo, that Palpatine is Naboo's former senator, and her friendship with and marriage to Anakin, but it's still the characterization we got.
Padme's characterization is all over the place throughout canon. What her actual beliefs are and how they balance with her personal interests and pragmatism is really anyone's guess.
Then throw in that she is a mother with newborn twins and how that will affect things.
It also depends on how pragmatic Padme is willing to be. I mean Palpatine didn't commit a coup or something, the Senate legitimately and legally turned the Republic into an Empire and named Palpatine Emperor. Sure, he rigged the game from day one but as far as the public and the Senate itself is concerned; it was 100% legitimate and legal.
This isn't the Empire after two decades of rule and repression, or the Empire after it has blown up one of the galaxies most prominent core worlds, or the Empire after the Emperor has dissolved the Senate.
This is the Empire immediately after an attempted Jedi coup against the most popular politician in the galaxy, one who has just defeated the CIS, one who is publicly seen as anti-corruption and pro "the little guy".
The Republic was a shit government for basically everyone, and a lot of the reforms that the Empire made were seen as (and were in fact) good things from the viewpoint of the average citizen.
Any kind of large scale revolt is an impossibility at the time, the GAR being fully on Palpatine's side and the CIS being fully defanged.
I could see Padme being pragmatic enough to decide that the best chance of actually throwing Palpatine down and restoring democracy is to stand shoulder to shoulder with Anakin and play the game from the very heart of the Empire. As far as anyone knows, Palpatine will eventually die of old age. And Anakin is both his apprentice and the commander of the Empires military forces.
Play the game, temper Palpatine's evil to the extent she can, and prepare to replace him (either via overthrowing him or by simple old age seeing him off) before restoring the Republic.
I mean a living Padme with the twins and a healthy Anakin? She is the one person that Palpatine absolutely cannot move against, he does and he guarantees that Anakin and him have their fight to the death. Moving against the twins? The same.
So long as Padme is at least nominally and publicly loyal, she is basically free to do what she wants. She is free to make herself the beloved face of the government to the public, the mother of the Empire, the Just Queen, and whatever other monikers seem useful; and Palpatine, again, can't really do anything about it.
Hell, the real baller move would be Ashoka Tano walking up to Skywalker. I mean she wasn't a Jedi at the time, and Anakin is unlikely to be willing to just let her be killed. Making her Padme's/the kids bodyguard would be hilarious. And, given the situation, Palpatine may well let her get away with basically neutrality so long as she is willing to publicly swear fealty and condemn the Jedi.
