I don't think I've actually seen the original film (from 1950), but I'm familiar with the basic story, and that's all you really need to know to follow this one. I'd describe this as a cross between "Cinderella", "Back to the Future", and "Men in Black"; it's a fairy tale with an SF twist to it. The animation has quite a classic style to it, which I liked - apparently this was the last Disney film to be hand-drawn.
This film picks up a year after the first one finished. Cinderella has married the prince, and they are celebrating their first anniversary, while her sisters (Anastasia and Drizella) are left doing the chores for her stepmother. Unlike pantomimes, this film never explicitly refers to "the ugly sisters", but they are a bit ... homely by comparison to Cinderella. This did make me think that it's perhaps less of an achievement when the most beautiful girl gets married first, particularly if she's got a fairy godmother backing her up. This film basically redresses that balance.
So, Cinderella and her new husband rode off into the woods to meet the fairy godmother. Anastasia spotted them, and realised what had previously happened. She then got hold of the magic wand and accidentally turned the fairy godmother into a statue. (If you pay close attention, the transformations aren't completely random: they're based on casual comments that Anastasia made.) However, her mother had bigger plans, and turned back time to when everything went wrong for them. This was the morning after the ball, when the prince's posse were searching for the woman who'd fit into the glass slipper. At this point, the three of them (the two sisters and the stepmother) had foreknowledge of future events, but they were the only ones. It's a bit like "Groundhog Day" in that respect, except that there aren't multiple loops of the same day.
In addition, they still had the magic wand, so they could use this to change events, starting by adjusting the size of Anastasia's feet so that she'd fit into the glass slipper. She was then swept off to the palace, which came as a bit of a shock to Cinderella; the stepmother smashed her slipper (the one she wore home), to destroy the evidence.
I do wonder whether the writers of this film have previously read "Witches Abroad" (by Terry Pratchett), since there are some similar ideas here. For instance, there's a conversation between the king and the prince which goes like this (paraphrased from memory):
King: "Dignity, grace - these are the things you should be looking for in your future wife, not her taste in transparent footwear!"
Prince: "It's not the glass shoe, it's the woman who wore it."
King: "But there must be hundreds of girls in the kingdom who are size 4½."
Prince: "It's all I've got to go on!"
When the trio turned up at the palace, they hit the first stumbling block in their plan, since the prince didn't recognise Anastasia at all. (According to the flashback, Cinderella wasn't wearing any kind of mask at the ball.) The stepmother pointed out that the proclamation was quite clear on this; the slipper did fit her. This left the prince in a bit of an awkward position: "Yes, well, I'm sorry about this - it seems that there's more than one person with the same size feet. I'm very sorry, and I'll get you escorted back home." Time for the magic wand! The stepmother zapped him, so that he'd forget about dancing with Cinderella and think it was Anastasia instead. This is what reminded me of "Men in Black", with the flashy thing that would erase people's memories.
This led in to a couple of interesting scenes. Now that the prince was (apparently) reunited with his true love, he proposed to her (which she gleefully accepted) and then they went for a dance (where she didn't do quite so well). Meanwhile, the prince was a bit confused: he remembered what it had felt like when he held her hand the night before, but it didn't happen this time. So, the idea is that Cinderella wasn't simply in the right place at the right time; instead, they had some real chemistry between them, which was missing with Anastasia.
The king then took Anastasia off for a private chat, and showed her some paintings of his wife (presumably now deceased). He said that she trampled all over his feet when they danced, but that they still had a happy marriage. I thought this was quite sweet, and it certainly cheered Anastasia up. He then gave her a seashell, which had great sentimental value to him: the first time that he and the queen walked on the beach together, they'd reached for this shell at the same time, and then their fingers had touched. So, that comes back to the chemistry idea again.
More generally, I think that Anastasia is the character who actually changed the most during this film. Initially I thought that they were just trying to distinguish her from her sister, but as the film progressed it turned out to be deeper than that.
Back at the castle, preparations were underway for the wedding. The two sisters didn't show the decorum that one might expect (throwing food at each other), while their mother was quite rigid in her social climbing aspirations. I think that you could draw a parallel between this and certain real-life romances in the British royal family, but I doubt that it was intentional on the part of the filmmakers.
Meanwhile, Cinderella managed to sneak in (pretending to be a servant), and was reunited with the prince, but he didn't recognise her. Fortunately, she still had the bluebirds and the talking mice to help her out. (Yes, I realise how silly that sounds.) Actually, I think that the squeaky mouse voices were the only annoying thing in the film, but they may be better suited to a younger audience, and are presumably consistent with the original film.
At this point, the story started to remind me of "The Little Mermaid", when Ursula put the whammy on Prince Eric (displacing Ariel). However, I think that this is a good thing, because it forced Cinderella into more of an action role. At the same time, her enemies are a bit more down to earth; although they're aided by magic, they're still ordinary humans rather than mythical creatures. I remember Scott McCloud talking about his comic "Zot": he said that the villains could be split into two groups, loud and quiet, and that the quiet ones were more dangerous. In this case, I'd say that the stepmother definitely falls into the quiet category.
Cinderella tried to steal the magic wand, but this plan didn't work and she was banished from the kingdom. I mentioned the animation before, and I particularly like the way that she looks when she steps off the wagon and gets taken onto the ship.
The prince was tipped off by the birds and the mice, although he had some difficulty in explaining this to the king. He caught up with the ship and brought Cinderella back to the castle with him. However, while she was getting ready for the wedding, her stepmother returned and used the wand to make Anastasia look identical. By this point Anastasia was having doubts about the whole thing: she wanted to marry the prince, but she was hoping that he'd accept her for who she really was.
The stepmother obviously wanted Cinderella out of the way, so she went for quite a clever inversion of the original pumpkin carriage. Cinderella was now trapped inside a giant pumpkin with the mice, and the roots acted as bars around the outside; a nearby horse was pretty much lassoed by the roots and dragged in against its will. It's not too brutal (given that this is a U certificate film), but it's definitely well presented. The stepmother's cat (Lucifer) was then turned into a human so that he can play coachdriver and take them far away. (Again, there are similarities to Greebo in "Witches Abroad" here; that novel took things a step further by saying that the horses could sense that he was really a cat, so they ran as fast as they could in an attempt to get away.) Cinderella wound up digging through the side of the pumpkin to free herself, and then leapt off onto the horse to avoid going over the edge of a cliff. I think that this struggle against adversity makes her a stronger character.
By the time she got back to the castle, the wedding was already in progress; she obviously wanted to get inside and stop it before it was too late. However, this is where the film subverted the usual paradigm. The prince readily agreed to marry Anastasia (believing her to be Cinderella), and then the priest asked Anastasia whether she would marry the prince. At this point Cinderella was heading up the aisle, but she wasn't close enough to interrupt before Anastasia answered, and that answer was "No".
I was hoping that this would happen, so I'm glad it worked out that way; since Anastasia was put on the spot and forced to make the decision herself, I think that this will be good for her in the long run. This may mean that the prince is a bit superficial: if he wasn't tipped off when he held hands with the "fake Cinderella", than that may suggest that it was purely a physical attraction rather than anything deeper. However, I'm willing to let that slide in the interests of Anastasia's character development.
The stepmother then intervened again, using the wand to get things back on track the way she wanted. However, the prince used his sword in the best tradition of He-Man to deflect the laser beam, er, magic bolt, so it wound up zapping the stepmother and Drizella instead. Anastasia then used the wand to turn herself back to normal and to restore the fairy godmother from her statue. She returned the seashell to the king, on the grounds that she didn't deserve it, but he said that she should keep it because everyone deserved a chance at finding true love. As I said, this is a nice feelgood movie, and it left me with a smile on my face.
The fairy godmother offered to restore the original timeline, but when Cinderella and the prince asked what was different she started to say "You got married" then said "Oh, never mind". So, no big reset button here: this film is the retcon ("retroactive continuity change"), effectively replacing the first one.
The end credits are fun - there's quite a catchy song from Hayden Panettiere (the cheerleader from "Heroes"), and some jokes that are aimed at an older audience (modified versions of famous paintings).