Dear Srimathi Mahalakshmi Krishnamurthy
Perhaps you are not aware that the rule is that the day of death does not count, and that the a-soucham therefore starts the following day.
That means the pelai-theetu starts on 14 August, not 13th. It continues till the punyaaha-vaachanam and accompanying graha-yajnya-homam are performed in your house. Originally these were done on the first anniversary of the death, i.e. the abdikam. These days, the shaasthrigals for the sake of conveninece, perform them on the 12th day.
You are perhaps aware of the normal practice that, since your husband's grandfather and the deceased's grandfather were brothers, your family cannot mix and mingle for one year with others of the community who do not have a-soucham, cannot visit temples, nor attend upanayanams, vivaahams, and other samskaarams, and so on.
One of the unique features of Veda-upaakarmam is that members of the same Vedam assemble at a sacred place like a riverbank, a seashore, an island, a temple, to perform as a group 1008 kaamo-kaarshi japam, deva-rishi-pithru tharppanam, Gangaa-snaanam, yajnopaveetha dhaaranam, kaanda-rishi tharppanam, Veda-paaraayanam, kaanda-rishi homam, jayaathi-homam, and other sacred rituals solemnly and seriously.
Accordingly, it shoud be obvious that your husband cannot "do the Avani Avittam" this year, whatever others might say.
Else, he will be breaching the rules and pollutng others with his a-soucham. Same applies to your sons if they are brahmaachaaris.