But your solution is to implement a law which punishes the victim, rather then doing anything about their presumed victimizer.
If the women who didn't want to wear the covering didn't want to wear it, what is stopping them from simply not doing it to start with? The answer of course is husband's, brothers, family etc. and probably that they'd be recognized in their community.
But this is someone's religion - a fair bit more important to them then the laws of the state in a lot of cases. So you haven't answered how you're going to protect those women from being targeted and forced to simply never leave the house, if they are being targeted by people who are forcing them to do something they don't want to.
Your law offers no solution to this - and again - implements itself by targeting the apparent victims it proposes to protect with punishment.
Setting aside that the government can stay the hell out of what I choose to wear, this is just a monumentally stupid approach to anything.
To do so creates conflict where there should be none, which is against the very purpose of a state.
At minimum, show the non-religious benefits of doing (or not doing) a thing and why it is relevant for the individual. Don’t punish the victim for doing the thing; if someone must be punished, make it the person imposing the action.
This is about swiss nationality and customs. Not about women's rights.
Just like you don't go to your greek neighbor's dinner party wearing a turkish flag, there are things you don't do when you are the guest at someone else's party.
The burka represents a lot of very nasty things, in countries that the overwhelming majority (60%) believe 911 was totally OK and beheading or stoning minorities is OK.
The fact is, you don't frown on people because they are spitting on some ideal of freedom. You frown of them because they don't get the basic rules of decency.
My house. My rules.
There are countries in Europe that are majority Muslim (Bosnia, Kosovo, Albania) where nobody thinks that, and where any kind of face cover is totally up to the choice. Turkey isn't that extreme either. Neither is Indonesia, Bangladesh, Nigeria, etc etc.
Why don't people ever think of those and jump straight to the Middle East? There are just as many Muslims living in India as there are in the Middle East.
Have you ever been to the beach? Have you noticed that in many western countries, all the men have bare chests and all the women are covering their breasts? Does this custom limit women's rights? Providing that women have the same legal right as men to go bare chested, as far as I can tell no rights are being infringed.
But maybe you disagree, do you think a law banning the wearing of bikinis by women would be a victory for women's rights?