rabbiofberlin, you mentioned a woman singing is not simple, I’ll even give an example: R’ Tuvia Goldstein zt”l held that if a family usually has women (wives or daughters) who sing at the Shabbos table, and you have guests over for Shabbos, the women were allowed to sing! I heard this from my uncle, who learned under R’ Goldstein zt”l for years in Emek Halachah. He told guests that was R’ Goldstein’s psak, but didn’t want them to be uncomfortable, so he would check before giving his daughters the ok.
Yes, I confirmed this psak with other talmidim of R’ Goldstein zt”l.