How to make magic training help my plot

....let me see if I can break down the problems you're sharing in each paragraph.

Your mentor-student-relationship bit sounds good and your system of classes on weekends and some during the week is great.
"Given the fact that I have elemental magic based on chemical elements a training system where they don’t learn to interact with others doesn’t make much sense either though, therefore the combined version." So instead of just fire, water, earth and air, or none of them at all, it's really broken down into oxygen, water, zinc, helium and what not. Okay. So you're not making classes where it's just the student and his or her mentor. He/she is in class with other students.

"I also had some scenes in ordinary school and her adept’s city" So is this like a public school? Corin wakes up at his home, brushes his teeth, gets his homework and takes the bus to school?

So it's a problem of character chemistry. Lenima can't grasp the teaching of mastering her element because Corin's element is different and can't find a way to incorporate how he learned to master his element to help Lenima master hers. Lenima is frusturated because she's not mastering her abilities because she possibly feels that Corin isn't teaching her right or not even trying. Corin is frusturated because Lenima is learning slowly, or not at all, possibly not even paying attention to his teachings. It's basically a problem of zero-communication.

I think if it's class based, and Lenima goes to Corin for sessions on a regular basis, then she can vent to her friends, Corin can vent to fellow teachers. Eventually, as schools work, word will travel fast and one or both sides will realize the problem. So yes, I think a pure magic scool setting with more interaction between various novices would help.

 

First of all I think you need to ask yourself why you feel to include the magic training. Is it purely a way to show the demonstrate to your readers the way the system of magic works or will Lenima's training with Corin advance the plot?

I'm guessing from what you've said you're going with the scientific table of elements rather than the traditional 4. That sounds interesting. I'm guessing there's science involved, mixing the elements? What can a chlorine magician do? What can you do with pure oxygen? Are the magicians limited to using their own elements or can they use others? (Sorry that's me asking questions now).

I was faced by a similar choice about a year ago. I felt I needed to show my readers the system of magic by demonstrating it at a training school. I had my MC, who is a fire magician being asked to take a class of inept magicians at the Fire School and bringing in a sub plot surrounding their progress. It helped me work out the magic system but didn't advance the plot. So I took it out and decided to allow the magic to speak for itself during battles, healing etc.

I think if you're going to give Lemina's education substance you will need more than her moving from now wanting to using magic to accepting and being curious about it. That doesn't create drama. On the other hand if Lenima hates magic, perhaps due to trauma in the past, and struggles just to be in a class with magicians, in spite of her powers that might work. What if she's accidentally mis-used chlorine to harm someone, or it's painful to use and she's got to build up to augmenting her power. That would set her a challenge. What if chlorine magicians are looked down on by those who use the airy elements like oxygen and helium. I don't know the context but there's some ideas to jazz things up.

A teacher who's 'quite nasty.' Wouldn't work unless the teacher had a reason to be nasty. Have they got a chip on their shoulder because they're teaching instead of working as a proper magician. Perhaps they've got an element considered inferior to others or can't mix them properly.

I may be barking up the wrong tree entirely here, but there's some ideas.

 

I'm just going to toss out some random ideas.
The training sessions are a nice idea but what about private tutoring? for 1 on 1's if your not looking for the interaction.

Corrin may not have the techniques but could help her train to reach a certain emotional state in which she can further what she already knows.

What happens if your MC tries to practice on her own from frustration over corrin and meets someone who shares her element and may be willing to help?

What about element specific classes weekly? Where all element training takes place in the same day just different timeslots and maybe overlapping with other classes causing friction and or interaction between characters.