How can a wife be gently made aware of her excessive sensitivity regarding her husband's prioritization of his parents' wishes, and of her unintentional shortcomings in making them happy, while taking care not to provoke her sensitivity?

Filial piety is a great virtue, as indicated by many texts from the Quran and Sunnah (definition), such as Allah's saying: ﴿And We have enjoined upon man, concerning his parents, good treatment. His mother carried him with difficulty and gave birth to him with difficulty﴾ [Al-Ahqaf: 15], and His saying: ﴿And your Lord has decreed that you worship none but Him, and to parents, good treatment﴾ [Al-Isra: 23]. Also, the Prophet, peace and blessings be upon him, said: "May he be disgraced, may he be disgraced, may he be disgraced." It was said: "Who, O Messenger of Allah?" He said: "He who reaches old age with either one or both of his parents, and does not enter Paradise." Furthermore, the wife has rights over her husband, based on Allah's saying: ﴿And live with them in kindness﴾ [An-Nisa: 19], and the Prophet, peace and blessings be upon him, said: "The best of you are those who are best to their families." If you gently explain to your wife the rights of your parents and her rights over you, and that you are keen to give every rightful person their due, she will understand that she also has rights towards you, and this will encourage her to care more for your parents.