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Thank you for your enquiry.
Your wife's visa is a dependant visa on your visa therefore any changes to your visa will affect hers.So if as a result of your resignation your visa becomes invalid, so would any visa dependant on it.
The information you received from the Home Office is correct. But once your visa is curtailed hers will be too and she will not be able to continue her studies. If you are referring to the youth mobility scheme, entry clearance is mandatory and you can not switch into this visa while in the UK. As you are a doctor you cannot work with this type of visa and you cannot bring family members on this visa.