When I was in Darchei Torah, R’ Yaakov Reisman (Rav of the Agudah of Long Island) gave a shiur on this topic. The son of a Rebbe had gotten engaged during the beginning of sefirah (before Rosh Chodesh), and a vort was held at the yeshiva for him, with music. The shiur was to explain how to deal with such a situation.
R’ Reisman told us that if there is a wedding, there is a mitzvah to be misameach the new couple, so dancing is allowed, as the mitzvah overrides the minhag of refraining from dancing during sefirah. However, if it was just an engagement, or a bar mitzvah, one should not dance, as it isn’t a special mitzvah to be misameach anyone.