000646,
The Rambam seems to be saying that she could be lashed at the discretion of a Dayan: the exact words are “??? ?? ??? ?? ????? ????? ????? ????”.
I think when the Rambam say that the matter should be clarified according to the way the dayan sees fit, that is referring to the method used for confirmation (e.g., unrelated woman in home or neighbors, etc.), not that the Beis Din can do whatever they want with or without confirmation.
I do not think whatever the woman brought into the marriage is hers if she arbitrarily walks out on her husband. Doesn’t that only happen in the case of divorce? (I know I may be wrong here, please correct me if I am)
I am by no means an expert myself, but my understanding is that the principal of what a woman brings into a marriage remains hers, but profits go to the husband while he supports her. For example, if the woman owns property, that property remains hers, but the husband is entitled to the rent income while he is supporting his wife. If they separate and the husband is no longer obligated to provide for his wife, she keeps the property and takes control of the profits.