i disagree. Nagisa did have some mistrust, but she moved to resolve it, albeit poorly. She tried to address an issue. I found it preferable to letting it fester. The mistrust is arguably reasonable as well. I'm sure most people would feel some kind of unease if their significant other spends a lot of time with another person who happens to be very hands on.
I think Misaki's situation is getting "lost in translation" so to speak. Being an AKB48 fan, I think I can understand where she's coming from. Misaki's close friendship with Ayane is part of her "character," the way she presents herself to her fans. It's like the friendship between Mayuyu and Yukirin from AKB, to name an example you can google. Can you imagine what would happen if Mayuyu suddenly stopped being close with Yukirin? It would definitely have a negative impact on her career as an idol, since that friendship is part of her "character." Likewise, Misaki can't really stop being close to Ayane. The only possible solution would be to quit, which is why Misaki says Nagisa basically wanted her to quit being an idol.
This situation is similar to date an actress and complain she has to kiss other people on camera. That's part of her job, and she can't possible refuse any roles that include kissing if she hopes to have a successful career. As her parter, you have to suck it up. Or you shouldn't have gotten together with an actress to begin with.
Likewise, if you're gonna date an idol, you gotta know what you're getting into. Otherwise it's best if you don't even try. Heck, idols can't even date openly, so you wouldn't be able to go on dates or even walk around. Dating an idol is not easy, and Nagisa clearly wasn't ready for it.