At the moment it seems that demand exceeds supply, with both breeders and rescues, so many breeders have rather long waiting lists. That means that there is likely to be disappointment for some would-be buyers.
What did you write in your email? Did you:
Give a summary of your family situtation, including ages of the children
Your experience with dogs and with the breed,
Your ideas about raising dogs,
Mention that you have researched both vets and training schools (if you don't already have those), including a 'Kind und Hund' course if your children are young,
Mention permission from your landlord if you have one,
Give a description of your property, including size of both house and garden and security of garden,
Specifically ask for an appointment, suggesting a few possible dates, or indicate flexibility at his convenience
If not, write again with all that. It shouldn't be a long mail, simply a summary to show that you are keen and ready to do the very best for one of his pups.
If you do get hold of this breeder, mention again the above - stressing above all else your readiness to give his pup the very best life possible. Whether it's involvement in dog training, in sports or club life, or just ensuring that his pup is guaranteed an all-around happy healthy life as a valued family member - good breeders want above all else to know that their pups are in the very best of hands. Stress how those hands are yours.
In a competitive situation - which is what acquiring a dog is at the moment - it's not enough to just register interest, you have to somehow stand out from the crowd.
If the breeder is not responding, it may well be that he already has a long enough list and does not want to take the time to assess more people than he likely will have pups for in the next 1-2 years. Dodging your calls is not polite, certainly, but take that as a sign that it might be time to move on.
I would not put all my eggs in this one breeder's basket. It might not be meant to be with this particular breeder, so start contacting other breeders and make inquiries. Also look outside of Switzerland, with the German counterpart (the VDH is the SKG equivalent) also with French, Italian, and Austrian breeders. If you have the means to travel - because a good breeder will require several face to face meetings - look even further afield in Europe.
(Do not, under any circumstances, go with a breeder who ships dogs, uses an agent, or does not require you to travel. First sign of a dodgy battery production facility. These must be avoided. I cannot stress this enough!)
It has always been a bit difficult to get a dog from a Swiss breeder, but now more than ever. There simply are not that many active breeders here.
(IIRC a BLV article, more than half the dogs in Switzerland come from other countries. I mention this to stress that it is perfectly normal to look outside Switzerland, you would be in good company doing so. It just takes a bit more work on your part.)
If this looks to be a long haul project, try to find out if any of the breed club activities are open to the public, and attend those. Doing so will not only educate you to how things work in the breed club, but you also might have a chance to meet other breeders. Networking can help.
Another networking tip: If you meet other owners of this breed while out and about, strike up a conversation, ask who their breeder is. And ask how they went about making contact. Sometimes owners who already have one of the breeder's pups are willing to help you make contact.
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I empathise, I truly do. The decision to bring a puppy into the family is a highly emotional one. You prepare the family for this big step, all ready to go... then find that actually getting the puppy is more difficult than you imagine. It's tough.
Please, if you are rejected by one particular breeder don't take it personally, as it is often really down to supply and demand. Just try to move on. It will be tough on the children, so do try to manage their expectations as best you can.
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Don't let this get you down, just keep trying other breeders. You will find your pup, hopefully sooner rather than later.
Wishing you all the very best.