Is it permissible for a woman to travel to visit her family without a mahram due to the husband being unable to travel, and is she sinful for not attending her father's funeral?

It is not permissible for a woman to travel without a mahram or a husband, due to the Prophet’s (peace be upon him) saying: "It is not lawful for a woman who believes in Allah and the Last Day to travel for a day and a night unless she is accompanied by a mahram." Therefore, it is not permissible to travel to visit family except in the company of a mahram, unless there is a necessity. Consoling family is desirable (mustahabb), but there is no sin in omitting something desirable. Hence, you are not sinful for not going to your family to offer condolences, especially since traveling to them without a mahram is not permissible according to the majority of scholars.