Is the marriage valid if the brother of the bride, acting as her guardian, says "My client (muwakkilatī) instead of my ward (mawlātī)" during the ijāb (proposal), and the husband says "Your client (muwakkilatukī) instead of your ward (mawlātukī)" during the qubūl (acceptance), given that all conditions and pillars are met?

The marriage contract with the aforementioned wording is valid, for what matters are the intentions and meanings, not specific words. Any wording that conveys the intended meaning is sufficient, along with specifying the spouses by name, اشاره (pointing), or description. The important thing is that each of the contracting parties hears what makes it understood that the intention is to establish a marriage contract.