Here's what I think about your being afraid that you will never be able to show her that you do appreciate her. What you are feeling is akin to the kind of "mistake" that you were making at the beginning of all this, the kinds of mistakes most of us make at first.
Which is, you're stressing about it too much and trying too hard to prove something to her she doesn't believe, or want to believe right now. It's like a form of pursuit, even if your simple intention is to show her that you DID appreciate her all along and even if your wanting to show her this is basically independent of wanting to get her back.
You say you are afraid that nothing you do will earn her respect back. Again, I think the worst thing you can do is fear this. Just relax and take a step or three back in this regard too. You've come a long way, so just continue to be a good dude, great father, and always treat her GOOD when you do see her. Repeat, just aim to treat her GOOD. That gives you the relaxed demeanor you need, not just to hopefully have a shot to get her back but to simply keep you on an even keel that doesn't smack of fear as you go about your daily life.
M-34 XW-32 D-7 Found OM's presence 4/09 Separated 12/09 Divorced 8/10 GREAT relationship as coparents since 8/10