Need To Detach, But How?

[NASCARDaddy]

I did have another text convo with W this morning that she initiated. I started out trying to validate and just stay neutral but it ended up not going so well. Perhaps you could evaluate what I did right and what I did wrong and give me more pointers. Here is the relevant parts.

Me: Is your mom going to be at the house today? I would like to give her the money back since I was not supposed to keep it. It would not have been enough to take you to the movies anyway because I only kept $4 and that is how much one ticket costs at the new theater. I thought they were going to be $2 each.
Her: Seriously? This is what you want to talk about?
Me: Yes. I don't want there to be anymore friction between us then there already is. I am sorry that I upset you.
Her: No. You are not.
Me: I understand that you think I am not sorry. I really did not mean to upset you.
Her: Yes you did.
Me: I understand that you think I did. I understand that you are upset so I will talk to you about this another time.
Her: Just like Friday and yesterday. You think I will relent if you upset me enough. Talk about what?
Me: I understand that you think I am trying to upset you and pressure you into taking me back. I am sorry that I made you feel that way. I will talk to you about giving your mom the money back another time.
Her: Whatever, You understand nothing because if you did you would stay out of my business and sign the papers.
Me: Actually I do understand how you feel; I understand a lot better than you think. However I cannot keep having the same fight with you over and over again. So please do not try and pull me back into it.
Her: Whatever.
Me: What is whatever?
Her: Just that. I am not in your business. I did not say anything to the bishop* about you, like you did about me. AND, you do not know what you are talking about when you did.
Me: What did I say about you to the bishop? How am I in your business.
Her: Whatever.
Me: I'm sorry but that doesn't tell me why you are upset.
Her: It is not your business. Just sign the papers.
Me: First of all it is my business what I supposedly said or did that has you upset; just like it's my business why you needed my mailing address. Secondly I will not sign the papers. If you really want this divorce then that is fine, but I will not let you bully me into giving you an out for the guilt that you feel for doing it. Finally, when you are prepared to discuss things with me like an adult rather than like a middle school student who refuses to say anything but whatever and it's none of your business then I would be happy to talk to you. Until then I will say hello when I see you but I have nothing more to say to you.
You can tell me all you want what a horrible person I am, but if you tell me it is none of my business why I am then I have to believe that the problem is in you and not in me.
Her: Can I count on that? Seriously, guilt?
Me: Yes, guilt. It is the only reason I can fathom that you filed for divorce but keep pushing me to be the one to end things, either by signing the papers or by going off with some other woman. Unless there is another man, and I don't believe that is the case. And yes, you can count on it. Just give me a schedule of when you are going to bring the kids by and all you will have to here from me is hello and good bye when you drop them off. At least until you are ready to talk to me more.

At this point I turned my phone off so I don't know what more, if anything, she said after that. There are points that I think I did try and validate her emotions. Perhaps I should not have tried to apologize for causing what she was feeling but to be honest I am a very empathetic person and if I make someone upset I want to make them feel better. That is one of the reasons I struggle so much to detach, because I know W is hurting, that I caused it, and I want to fix it. I know I screwed up when I said she was acting like a middle school student, even though it is exactly how my son that is in middle school acts. I probably should not have said that she was trying to bully me into signing the papers even though I feel that is a correct analysis of what she is doing. Being a skinny geeky kid growing up I have been bullied enough to recognize when someone is bullying me.

Thoughts, suggestions, critiques?