Problems With My Ex-wife's Boyfriend And An Orthodonic Appointment

Our eldest has an orthodontist appointment this morning, which my ex-wife scheduled. However, she is unable to attend. Her new boyfriend has been very aggressive in my interactions with him and has told both my children that he has a handgun and will use it on me if I cause trouble. I believe he is trying to prepare them mentally for him potentially shooting me. The children have also mentioned that he has mental health issues and that his medication is currently not working correctly. For the past month, they have been complaining about his increasing anger. He has only been her boyfriend for about three months and is already wanting to be treated as their father. My ex-wife also has mental health problems.
The real issue is that, with my ex-wife unable to attend, she is demanding that her boyfriend take her place. While I understand the difficulty of attending this appointment due to work commitments, I don't think his attendance is appropriate or safe given his threats against my life. My ex-wife insists he has the right to attend in her place. Since my attorney is out of town on vacation this week, I need a sanity check. Am I within my rights to refuse his entry to the appointment?
I have offered to forward any printed information I receive during the appointment to her and suggested that she can call or schedule her own appointment if she wishes to speak with the orthodontist directly. (Location TN)
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