What are the legal rights of the wife regarding the deferred dowry (mu'akhkhar) and the list of contents (qa'imah) if she is divorced after the husband discovers that she is speaking with her first fiancé?

You should make clear to your wife the wrongness of her actions and remind her of what Allah has obligated upon her regarding your obedience and treating you kindly. If she repents, ceases communication with the first suitor, and treats you kindly, then praise Allah and keep her, and treat her kindly. If she does not repent, then you may restrict her and refuse to divorce her until she ransoms herself from you with her dowry or part of it. If you divorce her, then she is entitled to her entire dowry, and maintenance, and housing for the waiting period, and mut'ah (a compensatory gift). It should be known that spying on one's wife is forbidden except in specific circumstances.