I Can See Your Answers.
Glad you posted - it's good to reach out when we're feeling unsure or overwhelmed with our life so that we can get perspective. It shows that you're open to finding a solution and in my books that means that you're already well on the way.
I can see your answers in your own writing, so all I'm going to do is mirror them back. It sounds to me like you're finding the way that he is expressing his NRE (new relationship emotions/energy) for her insensitive, and that you would like him to be more respectful and reserved in the way that he speaks about her to you. It also sounds like you would like to establish more "date nights" for the two of you so that you two share that same level of fun and special time together. I hear you saying that the status quo of just hanging out with each other, but not being engaged with each other doesn't really cut it when you can see him sharing that kind of uninterrupted time with someone else. That seeing that has made you realize that you want that as much as, if not more than he is sharing with his new partner.
I'm not hearing that you're closed off to him seeing someone else. But I am reading your meaning loud and clear; you need him to make more of an effort to create special time with you, and to be less effusive about the way that he feels about her with you. You'd also like to have him check in with you/build a schedule so that you feel involved in the choices of when he's going to spend the night with him.
It's my personal belief that poly works best when everyone feels comfortable, and nobody is being selfish with NRE. I also believe that you do have the right to have your concerns heard and be taken seriously, and to feel safe, respected and loved during your relationship with, or without a secondary partner in the mix.... but ESPECIALLY now that there is a secondary partner in the mix.
Glad to see you on here. Cyber-hugs!