If your wife's hours have been cut, (not just that they have told her they may do this, or that they are planning to do this, but when it actually has happened,)she needs to file for unemployment insurance at that point. She does not need to quit, resign, obtain permission from the employer to file a claim or anything else. She will just file for benefits, telling the unemployment system that she has been working 30 hours per week, and now her hours have been cut. They will look at how much she has made in a Sunday through Saturday week, regardless of how she works or when she is paid or how she is paid. Any time she is working all the hours that are available to her in a Sunday through Saturday week, and yet she is making less in gross wages than she would be able to draw for a week of filing for unemployment insurance, she will be entitled to partial unemployment benefits. They (the unemployment system) will explain exactly how it will work.
If she is formally informed by her manager that she will from now on be working 4 hours a week, with no benefits, she needs to tell them no thank you, and officially quit the job and file at once for unemployment insurance and tell them exactly what was told to her by the employer, how her hours are being cut and her insurance benefits taken away. This is "forcing a quit" and she will have a much better chance to draw unemployment insurance if this happens. If they say, work the new extended hours or you are fired, same thing, she needs to file for unemployment insurance immediately.
However, YOU stay out of it, she will need to file her own claim and speak for herself, and by no means does she bring up to the unemployment system that she feels she has been singled out because of the milk expression situation, or because she reported the nepotism (not illegal by any means here) or anything else like this. Unemployment deals with the reason why you are no longer working, whether or not you are out of work through no fault of your own. It is NOT the system under which people find justice for mistreatment they believe they have experienced due to EEOC or ADA or whistleblower or any other sort of protections or issues of this type. To try to bring in these issues will simply muddy up the unemployment situation.