Is Hallel Recited in a House of Mourning on Rosh Hodesh?

Is Hallel recited in a mourner's home on Rosh Hodesh? Of course, we recite Hallel as part of the Rosh Hodesh prayer service, but the question arises whether this festive recitation should be omitted in a house of mourning.

The work Meir Or, which documents the customs of mourning practiced by the Syrian Jewish community, comments (on p. 62) that Hallel is recited in a house of mourning on both Rosh Hodesh and Hanukah, despite the festive nature of this recitation, for a number of reasons. First, the private mourning does not override the public festivity of Rosh Hodesh. Additionally, if Hallel was not recited in a house of mourning, people might not wish to pray there, and the mourner would thus not have a Minyan.

However, as Rav Shemuel Pinhasi (contemporary) notes in his work Haim Va'hesed (p. 144), the mourners themselves do not recite Hallel on Rosh Hodesh, and should step out into a different room during the Hallel recitation. And thus although the people praying in the house of mourning recite Hallel, the mourners themselves do not.

Summary: Hallel is recited in a house of mourning on Rosh Hodesh, but the mourners themselves do not recite Hallel.