What should someone who would otherwise be saying kadish (whether as an obligation or not) do in a shiv'a (mourning) house? Should he say kadish along with the mourners (I'm asking according to the common custom that more than one person says kadish yasom at a time) as he would in a synagogue, or should he leave the kadish to the mourners only? I can't really think of a reason for the latter, but it seems somehow appropriate. Does anyone have a good argument either way, or a source for an answer?
The Shulchan Aruch rules (YD 393:1) that someone who is sitting Shiv'ah (who is generally not allowed to leave his house even for mitzva purposes) is allowed to attend the burial of someone else (even unrelated) in the community from the third day of Shiv'ah and onward, and if the deceased doesn't have enough people to act as pallbearers and gravediggers then he can attend even on the first day and in a different community.
The ruling states that when he attends he is placed with the mourners and not with the comforters, such that the comforters who attend end up comforting all the mourners.
It would seem from here that a given mourner does not have a monopoly on attention even in his own domain.
If you will permit me to draw on my own practice and experience. I try to avoid this but on those occasions where it was unpreventable, I said kaddish quietly along with the mourners. As against that, when my mother-in-law passed away, I, and another brother-in-law were in the 12 months for parents and the three of us (2 brothers-in-law and I) stood up together to say kaddish together - as it were within the extended family. I suspect that there are many customs for this, and if you don't have a defined custom, go for "darchey shalom" - one could even say that that is more of an "ilui neshama" than the kaddish itself (as per the halacha that one who yields to another in leading services of saying kaddish (in a one kaddish sayer place) is as though he himself lead the prayer/kaddish)