Are the brothers considered sinful for misleading the questioner and concealing the truth about their father's death, and for not waiting for him to attend the funeral despite his assurance of being able to arrive by plane?

It is from the Sunnah to hasten the burial of the deceased, based on the Prophet's (peace be upon him) saying: "Hasten with the funeral." This is the general rule, unless there is a legitimate reason for delay. Among the reasons for delay is waiting for the deceased's family, provided the wait is not long or there is no fear of the corpse decomposing. What your brothers did by hastening the burial without waiting for you is permissible, although it would have been better to wait for you, given your imminent arrival and the absence of any fear of the corpse decomposing.