Is the husband’s informing his wife that his family’s words to him are considered as words to her, and if the husband’s family did not speak to the wife after a surgery she underwent, should the wife initiate communication with them, knowing that the husband’s father is the wife’s paternal uncle?

Your uncle should connect with you through a call if he can, and you should also connect with him. The Prophet, peace and blessings be upon him, commanded maintaining ties of kinship even with those who sever them. The one who maintains ties is not the one who reciprocates, but rather the one who connects with his kin when they cut him off. Maintaining ties of kinship is not limited by the Shariah to a specific method or amount; rather, the reference for it is custom. It is achieved through visits, calls, correspondence, and greetings, some of which are higher than others, and the least of which is to cease abandoning them and to connect with them through speech. A wife must be kind to her husband's family and help him in honoring his parents and maintaining his ties of kinship. Forgiving those who wrong you increases a servant in honor and is a path to attaining Allah's forgiveness and pardon.