TLDR: Very good movie, great music, best visuals in the series, weird English, and some characters get significantly less than others Overall, I'd say this is a much better movie than chapter 1 and if it weren't for a couple of major flaws, I would rate this similarly to the original Niji anime. However, what really makes this movie shine is the music - it is, in my opinion, the best music of any of the Nijigasaki anime. The artwork and art style are also even better than the original. And if it weren't for the awful drawn out English speaking sections and Karin basically beinga non-factor in the story (and also not getting a song), I would rate this at least a 9. However I'm going to give what should have been a 7/10 an 8/10 due to how great the music and visuals are in this movie.

Definite spoilers ahead:
While Kasumi was basically the main character of the first movie and also subsequently didn't get a song, in this movie I would say Rina is the main character and has the largest role in the movie. She gets 2 songs and essentially creates the major conflict in the movie, which is that the grand prix (School Idol GPX) gets shut down. The short version of the story is that Mia's sister shows up and wants to hear her sing, but after Mia's failed performance Mia's sister says it's time for them to leave Japan and go back to America. Rina, not wanting to lose her friend decides to throw a wrench in the event and essentially "hack" the event and then ends up shutting it down. - the only one in this movie who's performance was actually part of the official GPX was Shioriko.
I think this story is actually decent. The hacking scenes are as stereotypical as it gets, but I really loved the Rina character arc it creates - which involves a more confident and brazen Rina that so is hell-bent on keeping her friend from having to leave her and the group, that she essentially destroys the reason they are there in order to do it.

The only issue I have with this, is that Karin is a almost complete non-factor in the movie. She doesn't have a song, she doesn't really have any sort of impact on the movie at all. She's just exists. And I think it's kind of unfortunate considering Kasumi was given such an important role in the first movie, despite not having a song. Shioriko is sort of in the same boat as Karin because neither really get much story, but at least Shioriko gets a song - and a really good one at that, with arguably the best music video/coolest visuals in the movie.

As for Setsuna and Ai's story, it is also really good. It's a bit short and just offers a glimpse into Ai's admiration for Setsuna and a bit of a flashback into how Ai joined the group because of Setsuna's Dive performance in the original anime. It also shows a conflicted Setsuna that is questioning if Mia's sister is right and if it's pointless to be a school idol considering she won't be able to continue eventually. This then leads to possibly the 2 best songs in Nijigasaki's anime.

Spoilers over:
The story of this movie is really so much better than the chapter 1 movie, it's not even close. Chapter 1 barely had a relevant story at all, while this movie builds upon the characters we care about instead of trying to make new ones.

So that's essentially the good and the bad. Now here's the ugly: the English. I've seen people really complaining about the English in this movie, and they are not wrong. It is awful. Some people have criticized Mia's sister's VA for her English, but I mostly blame the English writing. I understand that they want it to be easy to understand for native Japanese speakers who probably don't really speak much English, but it always comes off as unnatural. Even Mia's English, who is voiced by a native English speaker, sounds weird and unnatural at times.
I wouldn't normally think a little English in a Japanese movie is enough to detract from the movie, but there's just SO MUCH that it is genuinely annoying and does make the movie worse.

Edit: After watching the movie for like the 7th time I had a bit of a revelation. The issue with Mia's english isn't just that it's unnatural, it's that she speaks Japanese in a sort of informal tomboyish way, while speaking English in a very over-formal and feminine way. Even to her sister; she bows in one scene when asking her sister to let her stay in Japan - which makes no sense. What American bows to anyone, let alone his or her sibling?
This is all in spite of her being FROM AMERICA. (supposedly). If she is from America and your second language is Japanese, you would expect her to speak even MORE informally in English.