Meeting his gf?

This may give me some hate but that’s ok.

So I have a 4 year old son with some sensory issues. His dad and I broke up while I was still pregnant, he moved out when I was 4 months along.

We went through hell and back and have gotten custody agreed on via court last year in May. 50/50 sole and physical.

But dad hasn’t been consistent with his days and I usually get the short end and end up with our son on the weekends and most of the week. My mom picks him up every day from preschool and my sons dad doesn’t work rn. He doesn’t pay his half of daycare dues and I could go on and on…

Well last year in April, he moved in with a woman after dating her for a few months prior. He’s often very manipulative and mean. He tells me that I’ll never be half the woman she is to him. He tells me that their relationship is real compared to ours. He says that he’s glad I never got back with him when he tried Bcus then he wouldn’t have met her. He brought her around our son without even warning me… which I know some of you will claim he has the right to do, which he does but I just wanted him to tell me.

He’s moved out of her home and back on 2x in one year of living there. And now he’s asking me if she can be on my sons pick up list at school. I’ve never even met her. My boyfriend thinks I should meet her, but I honestly don’t have a desire to. I know it isn’t her fault in any way. But I had a really terrible experience with him overall. He’s not a great person.

How would you proceed in my shoes?