You have to stop reacting to "seeing her hurt". She's not a kid you're protecting. She has to live her live and make her choices, and you don't have to like all of them and you don't get to protect her from feeling any of her feelings. She is wanting to be separate from you, so it's understandable if she communicates to you that she's frustrated or sad or mad about your decision to stay. You could validate that if she seeks you out to communicate that to you.
But you have a legitimate reason to be in your own home, and many people going through this find a way to carve out the space that they need from each other within the same home.
You have your own hurt to deal with, don't take responsibility for hers too. Respect that this is probably hard and painful for her too. There was probably a long road that led to here or she wouldn't be making the decisions she's making. I think the goal is to feel empathy and compassion, but not responsibility, for her feelings.
You post sounded like you have a pretty good grip on your emotions. Be sure you take the time to feel them too, when you're not around her. Take care,
Adinva 51, S20, S18 M24 total 6/15/11-12/1/12 From IDLY to H moving out 9/15/15-3/7/17 From negotiating SA to final D at age 50 5/8/17-now: New relationship with an old friend __ Happiness is a warm puppy.