Kiddush for the Birth of a Daughter within Thirty Days of Mother's Passing

Is it permissible for a mourner to make Kiddush in the synagogue for the birth of his daughter within thirty days of his mother's passing?

If it is the first Shabbat after the birth and it is customary in the place to make Kiddush on the first Shabbat after the birth. If not doing so would appear as public mourning, then Kiddush should be made in the synagogue. However, if it is not the first Shabbat or there is no custom in the place to make Kiddush on the first Shabbat after the birth, then Kiddush should not be made.

Kiddush for the birth of a daughter is considered a seudat mitzvah because it is done to thank and praise God for His kindness to us. See Azmera Leshimcha, issue 23. Regarding eating, the later authorities are divided on whether there is a prohibition of public mourning during the thirty days and twelve months. The Shach in Siman 393, Sif Katan 7, and in Siman 400, Sif Katan 2, as well as the Biur HaGra there, Sif Katan 3, and the Chayei Adam, Klal 169, 9, and other later authorities hold that mourning during the thirty days and twelve months is observed even publicly. However, in the Gilyon Maharsha 393, Sif 4, and the Yaavetz in Shu”t, part 2, Siman 180, and also in Shu”t Pnei Yehoshua, brought in the Gra”z Margaliot, letter 26, and Pitchei Teshuva Siman 391, in the name of Adnei Paz, and other later authorities hold that mourning during the thirty days and twelve months is not observed publicly, and this is the custom, although there are those who are stringent.