I can understand the stress of the position that you are in at the moment.
Not answering your question at all, but something that I have often considered over many years: private schools - why? If people can afford them, okay, but for those who have never had that option, sending the children to a public scholl still works out, with children graduating and going on to further education, satisfying careers etc.
IF I was in the position of being short of money ( have been) and had children to educate, I would be using the public system of whichever country. (did that) If I found that that my child was only going to do well if sent to an expensive, fee-paying school, I would be having a serious talk to that child about the financial options ( have not had to do that) and what could be done with the money instead of it going on school fees.
One incompatible teacher/student relationship, or even one year of underacheivent, does not make a whole system bad.
Yours is the second case this week where I have heard of a parent on diminished finances, giving a child's private school education as one of the reasons for moving countries. If those children can do well in the private system, they can also do well in the public system, whilst saving the family 25,000 + per child, per year. That could make a hge difference to your family finances.
Now, back to your post: I am a bit unsure - you said your wife is refusing to leave Switzerland. However, you are talking about schools back in her home country. Is she willing to go back there? Or is what you are hoping she will be her only choice if she cannot keep her B permit after you leave? Is that the country that you are hoping to be gatting a job?
What are the other options? You working out of Switzerland, but coming back often enough to keep the C permit, so that your wife can continue to work here on her B? ( and hopefully her work going back to 100%)
You looking for work in a different field here?
You continuing to seek work here in your field? ( cut expenses by going back to the public school system. )
What are your wife's reasons for refusing to move? Her career? The lifestyle? Children's education? ( irrelevent. They will adapt.) Or ( sorry, this is harsh) is it an excuse to put distance between her and you? Some relationships actually work better as part-time ones, than on a daily basis.
If you move for a job, she doesn't, and it works out, then great. If it actually causes more problems thanit solves, then either coe back, or have her come and join you because she wants to ( not because she is forced to.)
I wish you,her, and your children, a lot of good luck with your decision making.