I think my kids have a shot at Gymnasium if that is the direction they want to go but I have come to find out there are many options. Our oldest is now in 8th and we have met with counselors and teachers to help decide on his route. I have been really happy with the school here.
Good luck on your move here
If you want, drop me a pm when you are here and we could meet up for a coffee
At 10, our son qualified for an immersion programme in a middle school. He has to travel by tram to get there but because it's more than 1km from our home he is entitled to a free transport pass so he can travel alone. He is quite safe taking himself to and from school by tram (although I don't let him read books because then he'd forget to get off at the right place!). He is learning very fast and it is a bonus that he is alongside other children in the same situation, so they support each other. We had no say in his placement but we were very happy with it. He is entitled to one year of immersion learning and can be placed in our local school when we and the teachers think he's ready. We're aiming to have him in the same school as his sister for the next school year.
My 7 year old is in our local school. Apparently immersion classes only start at age 10, so she is in a mainstream classroom and gets small-group German lessons when funding allows. Currently she gets two German lessons per week, one during class time (so she misses out on the class activities at that time) and the other one afternoon when the other children finish at lunchtime.
I can't speak for all schools and teachers but we are very happy with their placements. The teachers are genuinely caring and work hard to help them integrate. They help with friendships and are happy to explain the inner workings of the education system to me.
One thing I would consider if you can afford it is putting the children into a Hort if it's available. It's a lunch programme so instead of coming home for lunch (which is standard) they stay at school, have a hot healthy lunch, and have organised activities or free play with their friends. I wasn't planning to but they are learning the language a lot faster because of this significant chunk of time every day where they are hearing the language while playing. Unfortunately it does cost a bit if you do 4 days per week, but depending on salary you can get a subsidy for it.
I expect our kids to go to Gymnasium and I don't think they will have any trouble by the time they come to take the tests. As far as I know they won't test my 10-year-old for a while yet. They haven't even formally decided on his class placement for next year (which will be interesting as he is very clever but very lazy )
There's another chance to be accepted into Gymnasium two years later as well and this may give your children longer to learn the language.
hth
You have mentioned that one of your child was 11 yo when he/she joined the swiss school . In class was he/she placed?