My two cents here. I homeschooled my first child for a year and we both benefited from the experience enormously. And, unrelated, earlier in his schooling he attended a French public school and had quite a hard time with his teacher who hit him with a water bottle or pulled his ear when he wasn't paying attention.
We took up homeschooling as a way to spend more time together and broader his (and my) education.
We left our half sabbatical stay in France a few weeks early to avoid further troubles with the public school system there. The language/cultural barriers were daunting and I already had my hands full managing my newborn and 3-year-old.
Now, peacefully settled in CH, my children all attend the public schools here and it is a matter of trust and communication and patience. We did change garderies three times last fall to find one that my daughter felt comfortable in. I think the Swiss teachers that I've met here are used to some pretty docile and law-abiding children. My children (American) are arguably a bit spirited and my youngest, perhaps like yours, is very attached to me (and vice versa

) I think her teachers find it unusual that I do things like still help her with her shoes, and don't expect her to clean her plate or say good-bye without lots of hugs

. They seem to think I oddly don't know better rather than realize that, being from another culture/mindset, I have a different viewpoint and believe and have experienced that when my children are ready, they will/do become quite independent and capable people.
I think it would be a shame for you to leave the school system before learning what the alternatives are. I agree with others that it would be important to communicate as best you can with the teachers/director of your school and try to work it out.
Your child will be learning quite a bit from this experience. If she sees that you are working with the community while having her best interests at heart, she will develop trust in both you and the people around her.
If you want to homeschool because you are committed to that approach to your child's education, well, you can both have a wonderful experience. But the public school (unless you have teachers who are behaving disrespectfully to the children) will provide your whole family with the opportunity to become part of your Swiss community.
Best of luck to you! Sorry this became so long but I've got several underfoot here and it's been a challenge to write through all the interruptions!