Can a Rebbe who is in aveilus for a parent, go to his students bar mitzvas?
He can attend the bar mitzva, but in a limited manner. He may attend, but he should not wear shabbos clothing, (unless his weekday clothing is not presetable). He should not partake in the meal, but he may eat non integral parts of the meal, such as friuts, salad, drinks and dessert but not cake. He may dance a little bit, if his not dancing will diminish the simcha of the bar mitzva boy. Additionally he should leave as soon as his absence will not diminish the simcha of the bar mitzva boy.
The laws of Aveilus pg. 206-207, and other poskim. Although over there he is talking about a very vclose friend and siblings, a Rebbe’s participation in his students bar mitzva can be significant to the boy ,as he looks up to his rebbe and his participating in the bar moitzva means a lot to him.