Trimming the mustache during the three weeks:[1]

One may trim any mustache[2] hair that interferes with him eating. [This applies even during the week of Tisha B’av.[3] However, some Poskim[4] rule that during the week that Tisha B’av falls in, it is forbidden to trim any mustache hair, even if it interferes with food.]

[1] Michaber 551:13; Tur in name of Ramban

A Mohel: A Mohel may trim any hair that interferes with Metzitza. [Kaf Hachaim 551:172 in name of Ikarei Hadaat 27:11]

[2] Michaber ibid simply writes hair of the beard that interferes with eating. However we are accustomed to forbid cutting any hair of the beard other than the mustache.

[3] So is clearly understood from Michaber ibid who in the previous Halacha regarding haircuts only prohibits it on the week of Tisha B’av, and on this he states that trimming the mustache is permitted; Lechem Hapanim 122:3 in opinion of Michaber; Kneses Hagedola 551:13; Mateh Yehuda; Mamar Mordechai 551:12; Kaf Hachaim 551:170

The reason: As the week of Tisha B’av is similar to Shloshim, and not to Shiva. [Poskim ibid] And during Shloshim it is permitted to trim the mustache. [Michaber Y.D. 390:1; Maharitz Geios brought in Tur 390]

[4] Kitzur SHU”A 122:4; Ateres Zikeinim 551:13 that according to the Rambam and Raavad, brought in Shach 390:1 and Beir Hagoleh 390, and so rules Beis Yosef 390, that even within Shloshim it is forbidden to trim the mustache