My mother is sitting Shiva for a sister. May I take a shower?
If you are in the same city as your mother then you should not shower until after Shabbos, or until the end of shiva, whichever is earlier. However, if you are not in the same city, you have no halachos. The reason for this is, since it is a kavod for our relative, that we are sharing in their pain. If the relative doesn’t live the child’s city, there is no kavod to them by your abstaining from showering, therefore then it would be permitted.
Rema Y:D 374-6, Pischei Teshuva ibid-4 in the name of Shut Adnei Paz 11, Divrei Sofrim 22-12,15.