So now we are properly introduced to Nodoka Toyohama, who is Mai's half sister. In the first conversation between the Nodoka, Mai & Sakuta you can seem a difference of composure comparing the half sisters. Granted, Mai & Sakuta have dealt with weird shyt like this before. At first glance, it seems simple that the sisters go about being the other until the situation resolves.
Of course, one thing that is clear is that the two sisters barely know each other. We can see that Nodoka idolizes Mai. One major issue with Nodoka is her mother. Basically, her mother was jealous of Mai's success. I assume that didn't bother Mai's mother, so I doubt it was much on Mai's mind as well. But it really gives out that Nodoka's mother was obsessed with beating Mai's mom. You get the sense the pressure was there for Nodoka. A part also has with how successful Mai is. Nodoka isn't as naturally talented as Mai at picking up stuff. One thing is quite odd Mai & Nodoka are famous, but their areas shouldn't impact on each other. It makes me think that while Mai was active, Nodoka was feeling pressured by her mom. Thus, when Mai was inactive, things felt better back at home. Then when Mai came back that pressure came back. I mostly believe this because I think Mai being Nodoka's idol figure is true. Plus, I feel the conversation with Saki might be a solid hint.
The sisters' lack of communicating with each other might just highlight the issue at hand. We even see Nodoka having a panic attack while doing one of Mai's shoot. Clearly, Mai cares because she asked Sakuta to check up on her. Plus, when Sakuta says Mai had confidence in Nodoka that she could do a good job leads me to believe that Nodoka doesn't actually hate her sister. I guess part of it for Mai also is that she doesn't know how to act like a big sister.