I wish you the best of luck, but I wouldn’t consider doing that to an academically gifted child, it could stunt her future growth considerably. As important as I think it is for her to go to local school in order to integrate properly, perhaps you can put just her into the international school in order to continue the academic path she is on? The others are young enough to start in the local schools...
If the matura language profile is chosen, then a fourth language is also required, eg this can be Italian (if French is the 2nd national language chosen), Spanish, Russian etc.
However, if she attends an international school, she runs the risk of not being able to make local friends. At least some of those who go through the international system never really cross the mental bridge into living Here (not back There). It's the children's / teenage version of the expat-bubble, and by the time they're young adults, some still know predominantly English-speaking people, which may still be okay at university, but will end up limiting their employment prospects afterwards, not to mention their sense of ever being at home, or at least settled-in-well-enough.
This could be remedied by joining clubs and societies of sport and other free-time activities near her home. There, she'd have the opportunity to speak German and build local friendships.
I think it's at least in part a question of how hard the child herself is willing to work, to do extra lessons, to catch up, to push forward, etc., possibly by repeating a year (no shame in that). It really is possible to get more or less into the flow of things within a year, and for a bright, disciplined child, it may even be possible to make it into Gymnasium (at the first try, or later).
Since "Do as I say not what I do" can be de-motivating, the child's likelihood of success is increased by how much of an example her parents will be to her, in their dedication to learning German and their determination to settle in, meet local people, embrace the opportuniteis, and make Here the whole family's emotional home.
I've seen families whizz ahead, and do well, once each family member is determined to put in the necessary work.
OP, what does your daughter think that she wants to do, given the options here in Switzerland?
OP, you can also put her in intensive German lessons while she is in international school. She can interact with her neighbors and join local clubs too. I also disagree about the students not being able to be engaged locally at an international school. I have some friends who are here for life and have put their children into international schools for the same reason as I recommended. Their kids are happy healthy members of the local society. Of course you know your daughter best, but there are issues to consider.
Edit: I have two brilliant Swiss friends who missed out slightly from getting into gymi. They have been unable to obtain a worthy job to match their intelligence throughout their entire careers. I am able to be hired into better roles than they are simply because I obtained a college degree abroad. The Swiss apprenticeship program is very good for many, but there are some downsides to it for those who could and want to do better than the system dictates.
Law&order is important in edu. ( Although not entirely en vogue)
Indeed. It baffles me why teachers aren't armed. Especially primary teachers.
She could mince it up, do both.
Oh, they are! Just not very conventionally.
Unsurprisingly, these are also the Cantons with the highest ratio of "eternal students" (grade not achieved after double the default duration) and Maturi who don't study.
Generally the more urban and prosperous cantons (GE and BS) are at the top, and the Uris and Glaruses are at the bottom. I imagine this says more about the type of kids than the teaching.