Is it permissible to attend mixed public events that include musical instruments and singing with one's spouse, and does this necessitate declining the invitation or accepting it, considering that the Prophet (peace be upon him) never refused an invitation extended to him?

It is not permissible to accept an invitation to an occasion where there is an unchangeable forbidden act, such as parties with musical instruments, singing, and mixing of genders. The wife is not obligated to obey her husband in such matters. If a person is invited to a feast where there is an act of disobedience, and they are able to denounce and remove the evil, then they must attend and denounce it. If they are unable to do so, they should not attend. If they become aware of the evil after attending, they should remove it; if they cannot, they should leave, based on the saying of the Prophet, peace and blessings be upon him: "Whoever believes in Allah and the Last Day should not sit at a table where wine is served." The Prophet, peace and blessings be upon him, refrained from entering a house where there was an evil, as mentioned in the hadith of Safinah.