Rthom, I can't help with the contractual issue, that's for others better versed in legalities than I am.
However, thinking about practicalities:
Is your dog a puppy, an adolescent, or adult? And do you know what your deadlines for course completion are?
The ZH mandatory Welpenförderung and Junghund courses are age-dependent, designed to address critical developmental stages. So if your dog is at either stage cut-off it would be better for your dog to find a solution quickly, so that your dog gets involved in age-appropriate training.
If your dog is already an adult, you'll have been give a date by which you need to have done the Erwachsene course. If a deadline is looming, as above, it would likely be the best thing for your dog to find a timely solution.
I'm all for standing on principle when I am the only one affected by the outcome. But whenever my actions affect my dogs' well-being, I have to think of them first - and then I tend to look for compromise.
So if you are facing deadlines, talk to the trainer, look for a solution that helps you get that certificate on time.
And if that means taking the class in German:
I started taking classes here with pretty poor German - and honestly, the experience was something of a lightbulb moment for me. It made me look at how I train my dogs in a whole new light.
Think about it: Your dog doesn't speak your language either.
To the dog, everything you say is just a wave of meaningless sounds... Think of how frustrated he must be at first, not knowing what it is you want of him, until he somehow starts to pick up cues and clues, starts associating sounds with actions.
Taking a class in German without understanding German put me in the same position my dog is in day in day out. The experience made me better understand the importance of tone, body language, signals, and association. Sometimes it is extremely helpful to stand in someone else's shoes - or paws, as it were.
Our trainer only conducts classes in German, but through the many years I have been attending her classes there have been many participants with less than fluent German - or none at all. And it works. There is always someone in the class who can interpret as needed. But as above, so much of dog training is visual and intuitive - you really are not at as big a disadvantage as you might imagine.
Added bonus: My German is still unimpressive... but my Hundisch is pretty darn good. Seriously, the Hundeschule is my Sprachschule.
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If you are not facing a deadline or age-dependency, then sure, go ahead and look for a remedy and another class.
However, if time is of the essence... at least consider giving the class in German a try. Perhaps negotiate with the trainer for something to offset the cancellation - say, some additional one-to-one lessons maybe.
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Just tossing that out there. Wishing you and your dog all the best.