I'm so glad you and your husband have found a way to make some changes and I hope things start to look up as you head to Switzerland. I just want to note that I had the opposite experience to you in the NHS. We moved five times (twice internationally) in four years, my husband had been in a very difficult job situ, and we have two small children. I was so tired and felt I couldn't cope with everything, no family nearby, and no close friends yet in a new area. I went to the dr. just to ask her to run some tests to see if the tiredness was due to anything else. She sat and listened for twenty minutes, asked a few questions, and then just asked me to give myself one more month. Run some blood tests and go one more month without making a decision to take medication/ or any change. (This was all with the caveat that if I felt worse at all during the month I would call her immediately). She explained about serotonin levels being low after a prolonged period of stress, and how your body needs to catch up. I began to listen to my body, sleep as long as the children slept at night (sometimes 12 hours) carefully watched my diet, and took at least one walk a day. After a month, I did feel better and actually began to smile again. So, in many ways, I am glad I didn't have to start them, or feel pressured to. The blood tests didn't show anything spectacular, I think sometimes we don't give ourselves credit for the stress we are under.
This seems to be really acute for women expats with small children, and then if money/ job/ immigration issues are also factored in, I think the stress levels shoot through the roof.
I'm sorry you had a bad experience with the dr. (I had a bad experience with the first dr. I ever saw on the NHS, but since moving to York, they've all been really good.)