Thanks, Rayne, I think this is excellent advice.
@CANbbp, you may very well find that your balance on that tightrope of looking out for your children on one hand, and letting them make their own way on the other, will become easier the more German you speak, read and write, and the more Swiss-German you understand.
I'd like to encourage you to get cracking and do your own German homework daily and visibly. Live out the integration you'd like your children to experience. As they Go Out There each day to learn, they might feel better knowing that you understand them because you are working hard on the same issue.
Be their example of the one who labels the furniture on Post-ist, in German, or carries around a little stack of flash-cards, or has downloaded a language app that you actually use while waiting anywhere. At least a few times a week, do a family vocab session. If anyone amongst you is competitive, that might be a motivation.
Demonstrate to the children that when you speak to strangers, or someone at an enquiries desk, or the doctor's receptionist, and most especially any parents and teachers you meet, you always begin in German, trying it as far as you can get. Doing this helps to shift the mind-set that "they" ought to be speaking to any of you in English. After all, for some, English may be only their third or fourth language. When a letter comes from school, face it squarely as a challenge, pick out any words you recognise, and then look up the others and try to learn some right away, before resorting to Google translate (a good second step).
One day, you'll step out of Migros and suddenly smile as you realise that the entire interaction took place in German! That's a really, really good day.