In the invitation letter, have you stated the period of visit & that she will be visiting Switzerland on vacation?
In the past 2 years I have had my as well as my wife's family visit us on visitor visa.
You could also clarify with your geminide if anything more needs to be done while applying for a visitor visa from your wife's end since it has been rejected once.
Then the reason for her visit wasn’t clear enough for the authorities as that’s what they’ve rejected the application on. Check back with them to see what you’d need to say/do to convince them to allow her to visit.
could you elaborate what were the documents submitted to the embassy and what exactly was mentioned in the invitation letter? Also can you tell us what permit are you on at the moment and when does it finish?
AFAIK , it is mandatory to mention the below in the invitation letter,
Confirmation by the host (business enterprise or private person), stating that the applicant has been invited Contact number(s) and address(es) of the host and applicant (first and last name, date of birth, and citizenship) The letter must be duly dated and signed (invitation letters by business enterprises must be signed by a person listed in the Companies Registry as authorized to sign) A note saying that the host will provide food and accommodation Any further information on the reasons for the applicant’s visit to Switzerland When applying to an embassy for a visa, applicants are required to prove (payroll voucher, bank statement) that they have sufficient money to cover travel expenses. If the host provides for travel expenses, accommodation and food, mention must be made too.
Are you applying with the Mumbai or Delhi embassy?
Call the Swiss embassy and ask them why they rejected the application and what you need to do to get her here. I have had quite a bit of communication with the Mumbai embassy and they are very prompt in responding.
All the best and I am sure it is some misunderstanding somewhere which made them reject the application.
A possible reason why the embassy would have mentioned that the intention was not clear is that your wife applied for visitor visa and not family reunification. Family reunification is for long term stay of family members and a much longer process - details for the same can be found online at VFS. Maybe the application did not specifically mention that your wife would be returning to India after visiting you for a short while and therefore she needed a visitor visa only. Best course would be to check directly with the embassy.