It all sounds positive in many aspects. Yes, it is tough having R talks and trying to navigate through this emotional minefield. Overall, you've held your own pretty darn good!
Two of the arguments we got into were about rocking chairs for the babies rooms. I was opinionated and dumb about the whole process. The chairs were for her and her comfort, but I was an idiot about it and made her feel disrespected and unimportant. I should have let her have any chair she wanted, in retrospect I was such an idiot about it and unable to look at how she felt about the situation.
In retrospect, it is a silly argument. Couples do argue over silly and small things sometimes. What I am hearing W saying here is that she does not feel like she is an equal partner in this process. For future instances, you would want to ask her thoughts and opinion on some joint purchases or decisions that have impact on you two or the whole family. I hope you are open to apologizing for this and telling W that you would be more mindful of this type of thing. THEN BACK THIS UP WITH CONSISTENT ACTIONS.
I did not take this as venting and waited and scheduled the procedure to happen around Thanksgiving. I mentioned this to her and she was upset and said she was not ready and wanted to wait a year. I cancelled the appointment. During the next year we never really had much of a discussion about having more kids. She later told me that she talked to the councilor at her school about the issue. We both were at fault about not bringing up a serious heart to heart discussion about children. I later had the procedure, which I thought (assumed) I had her blessing on.
I want to ask YOU this: Why did you feel that you had to have a vasectomy? What was the urgency from your POV? I mean it is not due to health reasons like heart surgery or some other critical surgical procedure. Having a vasectomy is an elective surgery. Think on this one carefully.
We talked about the kids being the most important part of this. She said she did her research and everything shows that staying together is the best for the kids. Then soon after that she looked at me and said "but I will not be in this marriage just for the kids." My interpretation of this is that I cannot just let the kids bring us back, I need to do my work.
Then become the best spouse that she would be a fool to leave. One way to address this is to try to include W more in decisions and choices that you are weighing on various matters such as child care, school, hobbies, work, purchases, etc. Saying "what do you think" would do wonders for W and your marriage.
She said she really feels that I don't know or like her, this being a result of my actions making her feel not respected.
Pay ATTENTION to this gem from W. What are you going to do going forward to address this particular concern for W?
Now that you've had this long R discussion, I am seeing that you are wanting to prolong this by extending more invitations to W. I'd say..."slow down" and pace those invitations. You would not want to inundate her with a gazillion invitations and smother her. Make her miss you a bit.
I want to say this as gently as possible with the goal of making you aware: this is not piecing or R. Your W isn't clear in either direction. Just leave her be to allow her time and space to process this talk.