christine.j

Some relatives of mine had actually done this, BUT: This was more than 40 years ago, they had to register the child at a first and a second residence and had to pay fully for both Kindergärten. He walked out of one of them once and nobody realized it, since they were so used to him not being there all the time. With the long waiting lists for any Kindergarten today, I highly doubt that it is possible.  Your child will be confused enough by the separation, don't have him get used to two Kindergärten, even if you somehow manage to have him accepted. He'll be the odd man out, not attending all days.

I cannot help you with the name of a school, but since you mention the school has to be near the home as a German rule: That's only the case for the first four years in elementary school.  The children are supposed to be able to walk to school, meet their friends in afternoon etc without being driven there. That's not always so today, but this was the idea behind this rule. From grade 5 on it doesn't matter anymore where the school is in relation to their home.

You know your daughter best and you can tell why she is unmotivated. But you also need to consider what kind of school we've had this year: Just a tiny bit better than last year. At least more teachers have learned how to teach online.   I have talked to several  students and just one girl said she had liked the online school better thanthe real one. She is a very organized girl with lots of self-discipline. In contrast many more  students said they  had hated being taught online.  Several said they had lost all motivation, the teachers didn't really care, they missed the interaction with their classmates etc. This is not a proper survey. I work for a Nachhilfe school and it was there where I talked to the students.