Sex before divorce

I need some advice. My wife and I are getting divorced. I've been addicted to porn our entire marriage (11 years)- viewing multiple times most weeks with very few months with neither viewing nor fapping. The last three years I've isolated myself completely from her except to have sex with her (5-7 times/week). Most days the only time we spent together was the time it took to have sex in the morning and then I would leave and go to work. She wanted to spend more time together but I feel like sleep is important and I've been a bit depressed so I've been going to bed at the same time as our kids the last few years. Weekends are busy with kids and extended family and projects I have so we didn't see each other much then either. She has taken on the brunt of any and all stress in our marriage- financial, employment, family etc. Earlier this year she decided that, since I'm not interested in anything she does besides the kids and I haven't made much effort to do anything to show her I love her (even though I do love her), I must only be using her for her body. She's very upset and hurt. She's stressed enough that she's physically starting to fall apart. I feel like I do love her and that we do have fun together and that that should be enough but since it obviously isn't, I will give her what she wants so that she can get better.
The problem I'm having is this: the last time we had sex was weeks ago. She was not her normal, active self (the sex has been incredible- we're very compatible) because she had an ovarian cyst and it was hurting. Suddenly going from every day to nothing on a note like that was very hard for me. I show her love and I feel loved and connected when we have sex and I'm desperate to feel that again.
I know that she still cares for me but even though I know she'd physically enjoy having sex for the last couple weeks of our marriage she is refusing. I feel rejected and it hurts worse than the divorce. She says that she felt objectified before but the fact that I'm so concerned about having sex up until the moment we sign the papers only confirms that to her. This has been the only thing we've talked about for the last four days. I've been trying to convince her that this is solely for connection and intimacy and to heal our friendship- so that I don't feel rejected and can move on- but she is not understanding that. She says that she's concerned that this is all my withdrawal speaking, that she still feels like I only want her body but I know myself and I know that if we don't have at least one more good sexual experience together I'm never going to be able to get over the fact she's leaving me.
She wanted to talk to our therapist about the idea of having sex even though we're getting a divorce but he doesn't know us well enough and I don't trust him to give good advice. She says she's concerned that this is just the manic phase of an addict- that I'm addicted to the chemicals released when we have sex- and that she is worried that I'll have to go through this again a few weeks after everything is finalized. If that's true I'm fine with it. I just want to connect with her one last time and I don't understand why we both can't just enjoy each other again- it's not like she isn't going to get something out of the experience.
She suggested that I ask for opinions here because you guys understand what addiction is like and what it isn't and maybe you'd be able to convince her that this was an okay thing to do. I don't think that this is a symptom of addiction. I just know that I need this so bad so that I can start to heal and I don't understand why she'll let me give her what she needs but she won't give me what I need. She's taking the kids to her mom's house for a couple days to let me "clear my head" but it's not going to change anything because I am thinking clearly. What should I do?