Personally, I don't think a separation is a good idea. It might seem like it'll make it easier for you to work on things but my experience is that all that time I thought I would have to work on issues, I instead spend on thinking about W. What's she doing? Who's she with? etc. And, if one of her complaints is that you've been emotionally distant then how does leaving address that? She's telling you right up front that she need to see some fight from you, some emotion and you're agreeing to a split.
My advice, take you heart out, stick it on your sleeve and prepare for her to step all over it. She sounds like that's what she needs to see, that you care and that you won't pull back when it gets rough. I don't mean showering her with gifts and ILY's but more projecting a feeling of caring and love. When she asks you to do something even if it's small, take it seriously and do it without being told twice and without telling her it's done. Let her discover it and then simply say You said it was important to you so I took care of it. Think about what's going on in her head and think about what needs she has. Try to meet those without her asking for them. If she calls you from work and complains about a crap day, maybe you can have dinner ready when she gets home. Or chores done. Or whatever.
I think (and I might get booed for this) that many women really want a man who will not take no for an answer, who will continue to love and care after they have given up. The best responses I ever get from my W are right after she tells me something particularly hurtful and I bounce back and pick up caring for her where I left off. They're tests and every time I show her nothing will stop me caring for her, it gets through like nothing else does.
Also, if you're already pretty flirty, maybe you should take it a step further. Maybe she's used to you flirting so that is more of the same for her but maybe she wouldn't be used to something more serious. I don't know how your relationship is but maybe seduction is more what you should be going for. That's flirting combined with confidence and intent. Flirting is fun and light, seduction is serious. Maybe she wants to see that instead. Again, this is something I have found to be true in my sitch.
