It seems the international school fee for 'three' kids would be one of your major spending, besides all the expensive price index in switzerland....
As the other member has said, do not rule out Australia yet. Sydney is a very nice place to live, nice air and environment..English is the native language so you got more choice of school including public school. Things are not expensive there at all; Transportation is easy even without a car; Weather is good too; well mix of culture (esp in Sydney); also a safe place for kid....(note that i'm NOT Australian
If I was you, I'd try to be more open-minded. Cost for home-trip is certainly a concern but instead of going 2-3 times /year. could you get your family to fly to sydney instead?