i don't think you are being too sensitive on the two issues you posted. one, your "friend' is too insensitive. imho, that was a very "out of order" remark. i'd reconsider that "friendship". you had just lost your mom to a terrible event. i'm sorry for your loss.
as for your supervisor, that is not only unprofessional but an issue that could be taken up with your human resources department. that decision is yours of course but i'd consider it. if nothing else i'd ask to speak with the supervisor in private... stating your position on how upsetting this was to you that she used profanity towards you in front of other workers. it would give the supervisor an opportunity to apologize and correct a professional wrong.