Q. Can the husband say kaddish together with the children, for his wife and their mother.
A. There are different minhagim and traditions. Although the obligation to recite kaddish, when there are sons is on them, some congregations allow the husband also to say if he so desires. Yalkut Yosef (Kivud Av Vaem 13: p. 599) adds that this applies to congregations where many say kaddish together.
Osrei Lagefen (p. 554) writes that it is “kedai” or worth it, for the husband to recite kaddish during the shloshim or yohrzait of his wife, even if she has children reciting it. Zichron Yitzchok (42: 23) adds also the rest of the year. The above is the tradition in many Sephardi and Ashkenazi communities also.
Horav Moishe M. Lowy Shlit’a maintains that indeed some have that minhag in Toronto also and he is supportive of it.
Horav Shlomo Miller’s Shlit’a opinion is that it should be recited only by the sons and not by the husband at all, as is the minhag of many communities.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a