If you have joint legal custody, and if there are no orders prohibiting him from scheduling mental health appointments, then he has the right to schedule it.
If you have sole legal custody, inform him that he is not to schedule any healthcare or mental health appointments on behalf of son.
If your court orders state that both parents shall be allowed to attend appts, then you have the right.
But you should think very carefully about it.
Your ex is going to pick a psychologist who he wants to influence. By the time the appointment rolls around, the psychologist may already be biased against you.
If you show up, you may find yourself in a very bad situation, where it's going to be very uncomfortable for everyone, and where you have no idea what the psychologist will later testify about you (e.g., "Son got visibly upset upon mother's arrival"... even if it was more about the stressful situation than you).
I've been through this experience before. I first advised my ex that I thought she and I should agree on a mental health professional for our daughter, prior to daughter ever seeing one. She ignored me and picked on that she went to a few times on her own.
I elected not to attend the sessions. If I had no contact with the therapist, the therapist would not be able to report any conclusions about my mental health.
After the sessions with daughter, I wrote to the therapist and requested a copy of the records regarding my daughter-- as my state and court orders both allow.
Therapist wrote back, saying that I can meet with her to discuss it. No way. I again asked for the records (which she had to provide by law), but she ignored me.
My ex took daughter to the therapist about once a month.
Six months later, our custody evaluator interviewed this therapist. The therapist reported her concerns about my "serious mental health issues" and that daughter should have very restricted contact with me, given that 3-year-old daughter was suffering from a stress disorder as a result of contact with me.
The custody evaluator noted in his report that the therapist said that daughter never met alone, that mom was always present, so what daughter told therapist was of questionable validity. Evaluator discredited therapist's perspective about me, given that she had never met me.
This nutjob therapist was tainted from the beginning. If I had met with her, she would have been able to form a defendable professional opinion about me, which would not have been good for me.
IF I were to meet with such a person now, I'd want to record it, to ensure nothing is misrepresented.
So, IF you still want to meet with that person, bring an audio recorder. Just explain that it's to ensure everything is remembered as it's said.
If anyone objects (the therapist, your ex), then apologize and leave.