In our sysnagoue, it is customary for a man to lead the Shabbat Musaf on the Shabbat immediately prior to a yahrzeit. My mother’s first Yahrtzeit is this coming Sunday. Am I permitted to lead Musaf this Shabbat (even though we don’t lead the services during the year of morning)?

Shalom - Whether a person in the year of mourning can lead the services on the Shabbat before the yahrtzeit is a matter of debate. There are two sides to the question. Firstly, as you write, there is a practice that the mourner not lead the Shabbat services during the year of mourning. On the other hand, there is a custom to lead (at least some of) the Shabbat services on the Shabbat before the yahrtzeit. The Divrei Malkiel (6:23) and the BeTzel HaChachmah (4:129) forbid it. While the Even Yaakov (48) and the Shevet HaLevi (Y.D. tinyana 161) permit it. The Minchat Yitzchak (9:134) rules that one follows the local custom. [source: Mourning in Halacha, R. Goldberg, 44:2]. This is a great opportunity to approach the Rabbi of the synagogue for his ruling. Blessings.