WIBTA for telling my ex-husband that his affair partner is never allowed to be around our son?

I (35F) was with my ex (35M) for 13 years. Two + years ago, I spent a year in and out of the hospital dealing with serious health issues. While I was fighting for my health, my ex had an emotional affair with his supervisor (32F). He eventually left me for her about 1.5 years ago.

We currently have an informal 50/50 arrangement (2 weeks on/2 weeks off). However, I provide all the after-school childcare because he works until 6:00 PM. So, even on "his" weeks, my son (10M) is at my house every single day until his dad gets off work.

My son does not know about the affair. He doesn’t know the real reason we broke up. I’ve kept it quiet to protect his relationship with his father because I don’t want their bond to deteriorate.

My ex hasn’t officially told me he’s still with the affair partner (AP), but he told mutual friends he’s "terrified" I’ll keep our son away from him if I find out they are officially together. Yesterday, he asked me to go to court to make our custody official. It’s obvious he wants a legal order so he can introduce her and bring her around during his time without me being able to stop him. I don’t care that they are dating, but I cannot stomach the woman who helped destroy my family while I was in a hospital bed playing "stepmom" to my kid.

I’m stuck. If I hold this boundary, he will likely tell my son I’m being "difficult." If I tell my son the truth to explain why I don't want her around, I fear I’m destroying their relationship. I want them to have a bond, but I don't want her involved in it.

WIBTA for holding this line? Am I being spiteful, or is it a fair boundary?

I am really asking for the sake of my son, but also for my own peace of mind. If I am exaggerating or overreacting, I would appreciate any advice. WIBTA for holding this line? Am I being spiteful, or is it a fair boundary?