More specifically, my cousin's husband and his family, neither of whom I knew very well, deeply resented this decision.

resented 是动词 resent 的过去式形式。resent 由前缀 re-（表示"再次"）和动词 sent（send 的过去式，意为"发送"）组成，原意是"再次发送"，引申为"对某事感到不满或怨恨"。resented 在这里表示"感到不满"的意思。