Q. An ovel during shiva that doesn't have a minyan at home and comes to Shul, should he daven for the Amud?
A. It is a mitzvah to hold daily services in the house of the deceased for it gives fulfillment to the soul of the departed, (Remoh Y.D. 384: 4).If a minyan cannot be gathered at home and the Ovel attends shul to daven and recite kadish, there are different opinions in the Poiskim whether he should be the one to lead the services. There are those who maintain that he should lead only services at home and not in shul, to avoid conducting himself with authority and headiness publicly. As an ovel he should rather be humble and unassuming.(Kitzur Shulchan Aruch, Migdal Hashen 68 – see also Kneses Yecheskel 44: 3 in regards to Midas Hadin).
Other Poiskim rule that since in our days the sh'liach tzibur does not pray as a substitute for the congregants, rather each one prays for himself, the ovel, even when mourning for all other relatives can and should lead the services. (Maharam Shik Y.D. 370, Shevet Shimon 376, Chelek Levi 133, Misggeres Hashulchan 384 et. al.).
This last is today the most common tradition. There are however, shuln that maintain the first custom.
Horav Shlomo Miller Shlit'a stressed that the shul and friends of the ovel should make every effort to gather a minyan as required, at the ovel's home.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a