This is a funny assumption. Why does Polonius think his is their relationship? Does Gertrude USUALLY give her son the business? Is she GENERALLY a reprimanding sort?
If the actual closet scene is any indication, it would seem to be the reverse. Hamlet would appear to be a rather bossy insolent son who likes to tell his mother what to do. Gertrude will trot out an attempt at a scolding but it fails in several ways. 1) Hamlet takes no heed of it and 2) It gets Polonius killed.
This taxing Hamlet home business is perhaps not the job for his mother. Especially since he is an adult and a would be king. I’m guessing it used to be Hamlet Senior’s job, back when he used to walk the earth with blood in his veins and his armor on.