Okay where do I start. First things first, I think there are many good reasons your daughter should go to a public school. One of them being that the teachers there are a lot more qualified to teach than you are. It's also good for kids to get familiar with the world the way it is and not the way you want them to see it. They'll have to deal with the real world sooner or later so it's better for them to learn about it now than later.
Also, regarding your questions "What is Freedom, Are We Free?"
Yes, you are free. But freedom doesn't mean you can do whatever you want. If that was true the world would be in complete chaos! Freedom means you have the right to do whatever you want as long as you don't violate the rights of others and as long as you fulfill your duties. Your daughter, by law, has the right to be educated and your duty is to allow her that. By homeschooling her you would be taking that right away from her since you're most likely not able to provide her the required, unbiased, knowledge.
So in my opinion, a public school is a much better idea than homeschooling although I'm not saying public schools are perfect either. All I'm saying is that they're better.
If you still think homeschooling is the way to go (which I'm assuming you are), then moving is probably the only way to go. Although in Sweden, as far as I know, you can request special permission in special circumstances, but I doubt you'll have much luck with that.