Two issues come into play in this case: the positive element of a minyan taking place in the shiva house and the problem of an avel leaving his house. We will deal with one at a time.
The Rama[1] writes that the deceased has nachat ruach (a spiritual “good feeling”) when people daven in the place that he died. Therefore, if the shiva house is where the deceased died, significant efforts should certainly be made to hold a minyan there. There is a difference of opinion regarding whether davening in a shiva house in his honor brings about nachat ruach when the deceased did not die there.[2] This element would not seem to exist at all when it is a separate minyan held in a different area of the building.
The Har HaCarmel[3] provides other reasons that it is good to daven in a shiva house. 1) Often an avel says Kaddish for the deceased (i.e., for a parent), and it is better that he can do this without conflicting with other mourners. The Har HaCarmel says that the minhag was accepted across the board, even when the avel does not say Kaddish. 2) It is forbidden for the avel to leave the house and the minyan thus enables him to avoid missing the mitzva of davening with a minyan. Let us evaluate, then, if the problem of leaving the house applies within the same building.
The Shulchan Aruch[4] rules that an avel should not leave his house during shiva. The Terumat HaDeshen[5] explains that he should focus on mourning, and this element is compromised when one leaves and interacts with others. Based on this reasoning, the Terumat HaDeshen allows one who needs to go from the shiva house to a nearby house to do so at night, when there is little activity on the streets.
Poskim considered the relative gain and loss of allowing an avel who does not have a minyan in the shiva house to go to shul. The Magen Avraham[6] implies that if he is leaving just to take part in a minyan, the mourner should stay at home. Note that the Terumat HaDeshen assumed that davening in shul presents more of a problem than walking home at night, because in shul there is likely to be interaction with others. This is different from people gathering in the shiva house, where the focus is on the shiva.
In contrast, the Eliyah Rabba cites an opinion that if the mourner is a son who wants to say Kaddish for the deceased, he should go to shul,[7] and many accept this opinion.[8] The Chochmat Adam[9] goes further, saying that it is logical that any avel who would miss davening with a minyan may go to shul. Although he seems reluctant to rule contrary to the Magen Avraham, he says that if the shul is in the same courtyard, so that the avel does not have to pass through the public domain, all agree he should go. A minyan in the avel’s building is no worse than that permitted scenario. This opinion seems to be accepted by later poskim.[10]
However, approval to go to the nearby minyan does not absolve one from making an effort to have a minyan in the shiva apartment, as those who are lenient regarding going out discuss cases in which it is a fact that the minyan will not be held there. Therefore, even in the absence of the problem of going outside or meeting anyone on the street, it is nevertheless proper that the mourner take part in a special shiva minyan for his deceased relative. Since different levels of difficulty and other factors may impact a particular case in a manner that we cannot anticipate, it is difficult for us to give an absolute ruling. However, either for the positive reason of nachat ruach or for the negative reason of leaving the house, a minyan in the shiva house should be strongly pursued and takes precedence over having the avel participate in another minyan.