Personal stepping over to professional?

I had a personal situation occur on the weekend. A phone call was placed to my daughters ex – singing a silly song that was inappropriate but not threatening any bodily harm. This comes after years of being hared by her and me never responding. She went to my place of employment and played the voicemail to the board of directors and demanded me to be reprimanded. They sent me a letter in full detail of how this was unacceptable. If I were to cuss out a grocery store worker – would that be reason to reprimand me too? Has my employer stepped over the line of personal and professional? What are my rights in this situation?