I’m a teacher but not a mother. I felt myself in a similar position than your wife for a time in my relationship, so I understand your wife’s situation, then, I’m not very good at relationships (I mean, handling relationships or knowing people, much less, about relationships functioning, I don’t have a lot of experience) so maybe I’m the last person who can give you a clue or tell you some words.
But, we have in common the thing about the anger and I would like to give you a little of support.
You are being very hard on yourself and it’s not a bad starting point at all. I can read how you are very aware of you not being ready, for X reasons to correspond your wife as she deserves in the past. I want to stress on the past on purpose. You are now a new person. You’re aware of your flaws. Often, behind anger is hidden frustration, fears, insecurities, angriness with ourselves, eventually pain. And we need to put a little of that outside to alleviate a little. To avoid being consumed.
The solution is not easy because it’s a whole process to learn to manage this anger. And if you fail in the process it’s normal and you must see it as a push to go back to your work again.
When you manage this anger you will feel each day better and stronger with more trust in yourself.
So there’s a gratification that will push you to go forward.

I don’t know if your relation with your wife has a solution but with your daughter, I’m so convinced. She is the normal age to feel reluctant her parents separate themselves and she will probably want to fix it up because she may feel responsible but with care and affection on part of you both, she will adapt to whatever the situation may be in the future.

If I understood well, your daughter call for her mommy even when she’s with you? And I’m sure you must feel the worst parent in the world. When you feel that remember that kids don’t have the knowledge enough to express things as adults and maybe through a remark that can sound us as a knife, behind this remark, there is the real message, hidden, like when you have to decode a message.
Always, ask yourself, what she is trying to tell me in real, what does she need? Without you feeling upset or disappointed. Be more open than ever to understand so you will be able to communicate effectively.

I remember my nephew saying to his dad that he didn’t love him. Nah! He was only asking a different treatment, a little more of attention. He is very sensitive and he felt rejected.

Coming back to you. How do you feel when your daughter ask for her mommy when being with you? What do you think she’s trying to tell you?
(No need to reply. I don’t want you to feel forced)

PS: My apologise for the long post but when the thing is about kids, I don’t know what happen with me. I feel touched.