Advice on boyfriend becoming friends with ex again...

About a month ago, my boyfriend of 1 year initiated contact with his ex-girlfriend. They dated for 4 years and were best friends for 4 years before that. When he told me they had started talking, I admit I was uncomfortable. I felt caught off guard, and the last time they had met up, about 3 weeks into our relationship, he had come back and told me he couldn't be with me out of loyalty to her. Apparently he had told her about me, to which her reply was, "Can I go home now?" Since then he said he couldn't talk to her until he was sure the romantic feelings were gone, as he had been really heartbroken when she broke up with him and had to return an engagement ring. I got over my insecurity with him talking to her, since he said he was exploring the possibility of having her be a friend again and I figured it was fine if they kept in touch and met up from time to time. Two days after talking, they went to get coffee. In the 3 hours they were out, he never mentioned me. When i asked him why, and said that it wouldve made me feel more comfortable with the situation, he said he felt badly for his friend and that he wanted to protect her. This made me feel like my feelings were less important. Eventually, after expressing ny feelings about it, i determined to get over it. Recently I have found out that they text all day long, every day. They have met up every weekend, the most recent time I had to leave his house so that she could come over, per his request. It also took him 3 visits with her to mention me, when she saw my bracelets in his room. He said that he started to tell her about me and that she asked him to slow down. I have tried to analyze the situation rationally. I am aware of some jealousy, and I know that she will know him in a way that I don't. I am okay with that, and I am okay with him loving her as a friend. I just feel like they have a secretive friendship where I am merely a name or idea rather than a reality. I trust him and know he is not having a physical relationship with her, but I am worried that there is something emotional going on that feels inappropriate. I am not usually a jealous girl, we both have friends of the opposite sex. I am not even asking for him to stop seeing her. I think it is fine to have each other in their lives, but something about this feels secretive. He knows I have been getting stressed about this and asked what I thought I needed to happen to feel more comfortable. I told him that I want to be integrates, to meet her. If she is a part of his life then she is a part of our life. If she is truly his friend then this shouldn't be a problem. I also said that I was overwhelmed with the pace they were going with rekindling their friendship, he said he wanted to take it slowly but it sees the only slow part is anything involving me. He barely responds to me via text yet they talk constantly. I asked him to please take it down a notch until I am more comfortable with it. Like I said, I don't want him to cease contact with her, but what is going on seems a bit excessive. He said a few days ago that I was his best friend, but it doesn't seem like it with his actions. His response was that I didnt trust his judgement and he is not ready for me to meet her. He said she might not be ready to meet me and he doesn't want to drive away someone who was his best friend. I tried to talk calmly with him. He told.me it wasn't up to him to fix my issues and that this doesn't happen in mature relationships. Also that just because he asked me what I needed didn't mean he was just going to do it. I feel betrayed and alone. I have never been in a situation where a boyfriend has started seeing his ex again or one who was a best friend. I am unsure of if I am justified or crazy. Any advice?