Are the exemptions to the requirement to work while on probation for full time parents who have a spouse that can financially support tem?

The best place to start is with the judge who placed you on probation.  Assuming your daughter is too young to attend school, set a hearing asking the judge to modify your probation so that you can stay at home with your daughter. 

Although I do not practice law in the State of North Carolina, here are my initial impressions.  While it may be possible to have your probation modified, as my colleague suggests, my advice is that until the order is modified you MUST comply with the terms of probation.  Since you indicate that your wife is a doctor and that you are financially secure, I would assume that you hired an attorney to represent you with respect to the underlying charges.  Therefore, I suggest that you consult with your attorney to discuss what, if any, options are available to you at this point to modify the current conditions of your probation.  Good luck.