Is it permissible for the husband's family to refrain from eating meat from the beginning of Muharram until the tenth of it, considering it a covenant inherited from their forefathers that must be adhered to?

Refraining from permissible things that Allah has made lawful, such as abstaining from eating meat on certain days as an act of worship, is considered a form of monasticism forbidden in Islam. It is an innovation (bid'ah) and a deviation for which Allah has not given permission. The Prophet (peace be upon him) forbade this and clarified that whoever turns away from his Sunnah is not of him, and that "there is no monasticism in Islam." Acting contrary to the Sunnah as a form of worship is innovation itself. Allah has commanded to worship Him only with what He has legislated, and unlegislated acts of worship are rejected and invalid, even if done with sincere intention.