I wouldn't say Anakin's turn was rushed at all when taking into account not just the foreshadowing in Attack of the Clones, but the women, and the children too! but how much being unable to stop something he knew would happen because of the Jedi held him back before. In that moment, it came to either allowing what he perceived to be the inevitability of Padme dying happen or risk the one chance to save her, with the motivation of Anakin wanting to have the power to save those he loved being something made blatant throughout each instalment of the prequel trilogy.
Alongside that, Palpatine's manipulation was validated in Anakin's mind when Windu actively went against the teachings of the Jedi by attempting to kill a "defenceless" Palpatine for his own personal reasons. Both AotC and RotS make it apparent that Anakin is also the kind of person who lets his emotions take the better of him in difficult times or when he's offered a choice (Killing not just the men, but something something too!, Charging at Dooku on Geonosis, Killing Dooku when told to Dew It, etc.) so all these attributes allow for this choice to fall very much in line with his character.
His immediate loyalties to Palpatine after this were less a sudden change and more an inevitability of having to live with his decision. This is made apparent when Palpatine says "When the Jedi learn what has transpired here they will kill us, along with all the senators." Immediately after this, Anakin agrees, which is perhaps the most important part in contextualising this. He also does this whilst standing straight and composed, showing he's not just being irrational about this and that this is his genuine belief based on his growing distrust in the order and seeing what happened when Windu went to what was supposed to just be an investigation into Palpatine. Also, keep in mind that "along with all the senators" would include Padme. The part Palpatine says before this is very important in understanding Anakin's state of mind too: "Because the council did not trust you, my young apprentice, I believe you are the only Jedi with no knowledge of this plot." This would be a very reasonable conclusion to validate Palpatine's words in Anakin's eyes when he was actively excluded from many standard aspects of the Jedi Order such as not being granted the rank of master (and having to take a seat) despite his accomplishments surpassing the majority of masters and such a thing having never been done before in the history of the order. Truly outrageous and unfair.
As for him going as far as to kill the younglings, this is another inevitability that was forced upon him with what's stated in the same scene by Sheev: "Do what must be done, Lord Vader. Do not hesitate, show no mercy. Only then will you be strong enough in the Dark Side to save Padme." A moment of emotion had forced Anakin into this and to go back at this point and risk losing everything would have made all he had done a waste. It's not as if he enjoyed what he did at the temple, as we see with his tears on Mustafar when he's finally given a moment to process what he's done.
As for his corruption and lust for power shortly after that, this is something that was building up ever since Attack of the Clones. He has always been yearning for something more than his current standing, feeling as though his natural talent demanded it when the Jedi held him back. Now, the title of Emperor is the only thing he can aim for when looking up and by that point he'd become entrenched in the Dark Side enough when killing the Separatists to achieve the trademark Sith eyes. With all that said, I'd say his turn was handled brilliantly.
Onto Windu's decision, it was indeed far from well thought out with several alternatives that could be made. It's important to note, however, that Windu has been portrayed as far from composed compared to his peers on the council. His first move at the Geonosian arena was to go into aggressive negotiations and hold Dooku at saber-point rather than any alternative and, when facing Jango, his immediate instinct was to go for the head. It's made clear through his actions that Windu is the kind of Jedi who prefers putting down a threat regardless of the order's teachings and, combined with his growing distrust for Palpatine, resulted in him using Anakin's revelation as the excuse he needed to take Palpatine down the only way he knew how.
As for Dooku and Grievous being jobbers, that's expected. The prequel trilogy is meant to be a concept-driven story about two things - Anakin's fall to the Dark Side and Palpatine's rise to power. Because of this, Anakin and Palpatine are the characters of which it's essential the movies' focus should be on and; whilst fleshing out and exploring the other characters in-depth would be nice, doing so for villains that were there to serve the purpose of being parallels to what Anakin would become would only make pacing messy in a movie that already had far more going on in its story than any other Star Wars film even after a lot of important scenes were cut.
Overall, the only flaw in RotS I'd consider to be pretty apparent would be Yoda having good relations with Chewbacca, which kind of screws up Han being so atheistic towards the Force in ANH, though it's not much more damaging than something such as, say, Leia sensing where Luke is without any training or Lando treating Han and co. as guests when the Empire apparently arrived before them in ESB, or Leia's "Somehow I've always known" in RotJ. Yes, I'll say Padme's death actually did make sense when you consider that the medical droids seemed fully focused on her health in terms of the pregnancy and it'd make sense for them to have not examined her neck (keep in mind how powerful Vader's force chokes are) and that she hit her head on the pavement when she fell.
