You may have missed this thread because the title suggests it is not about school but in fact it is.

Chances of casual work for my 16 yo daughter from UK ( EN only )

I posted a link on that thread(sorry German only) with options in Kanton Aargau. To be very honest, your children are at a difficult age to integrate into the local school system, particularly your daughter. Many would advise you to let your children continue with their schooling back home unless you know you are going to be staying here permanently, not just for a while, or your employer is willing to pay for international school. Have you asked?

If your children are not interested in attending university, which many children here do not, the local education system offers opportunities for young people to take different paths to gainful employment. My neighbour's son is an electrician, he did not attend university. Electricians are one of the highest paid tradespeople in Switzerland!

Teenagers are the most difficult group to relocate. I am not one to promote families living apart but there are times when putting childrens' educational needs first may mean living apart with visits during school holidays.

I know of a few teenagers who came but did not stay because they could not learn the language quickly enough, or make friends and were miserable. There are others who have managed but not without hiccups along the way.

Hope you find a good solution.