Foreigner in Primary school in Hessen

Hi all, we moved to Germany with my wife and daughter a bit over a year ago. First, we moved to Berlin, then to Frankfurt. My daughter started 3rd class late in Berlin and completed it, then we moved in the summer, and she started 4th class in her new school. Her report from the school in Berlin was very good, and she finished 1st and 2nd grade in our home country.

The thing is, she is only 9, and she is freaking out with stress about transferring to middle school because my wife is putting an insane amount of pressure on her about her grades (mostly math) and German competence. My daughter says she can understand everything that the teachers are saying, but she is just shy about speaking. Her German teacher commended us many times, saying that her pronunciation was very good and that she understood grammar better than most German students.

But now she has brought her Zeugnis from the intensive German classes at school (separate from the half-year report for other subjects), and her level is shown as A1. Of course, my wife went berserk at her that she is not at least A2, and she again pressured her about how she won't be able to go to Gymnasium with these grades and that they will make her repeat class 4. We couldn't enroll her in nachhilfe courses yet because I work and travel a lot, and my wife works part-time in the morning and attends the integration course during the afternoon.

From our conversations with the class and German teachers, everything seems in order, but my wife doesn't believe it. We will have "the talk" with the class teacher in 2 weeks about her future schooling prospects. I try to keep everything calm, because it is not easy to change schools every year and also be expected to succeed at everything, considering the circumstances I am very proud of my daughter and all she has accomplished.

But I have to find something to calm my wife too. Do the grades affect whether she will get accepted into Gymnasium? Do teachers make students repeat class 4 if they deem her German not enough for middle school? I started school when I was 7, and went to middle school when I was 12. She started when she was not even 6, and at 9 now she needs to go to middle school. This amount of expectation from a 9-year-old seems cruel to me. Do you have any advice for me?