What is the expiation for the tubal ligation procedure performed by the wife 22 years ago, which led to infertility, especially since it was done under the influence of the doctor and family, and due to ignorance of the Islamic ruling?

There is no specific expiation for this action. Its doer, if without a legitimate Sharia-compliant reason, must repent and increase in acts of obedience. For whoever was ignorant of the religious ruling, we hope there is no sin upon him, as ignorance is an excuse.