No, it can't, I'm sorry - honestly, for it to get to that point in the first place indicates a massive, massive lack of respect for you as a person. He says he loves you but if he did, he wouldn't have done it. You could say he lost control but could you imagine a situation where you were so angry that you would punch him in the face while holding your DD? And would he hit anybody else? His boss, perhaps? His mother? Or just you?
The remorse, proclamations of love and promises to change - especially things like doing anger management - this is all really really common behaviour after DV. Almost all men will react this way after you leave - it's far too early to tell yet if it's genuine (and sadly, it's very rare that it is.) Often it comes from a desperation to get you back - either because they like having sex on tap, cooking, cleaning etc done for them, or a fear of being on their own or that nobody else will ever love them, or a compulsion to prove that they still have control over you, possibly alongside one of these there will be a real feeling of love for you, but still it's lacking - love includes wanting to protect the person you love. It's about as far from hurting them as you can get. - But getting back to this, it's about wanting you back, not wanting to change. The reasons that led to the violence in the first place will still be there, and you'll always be on edge slightly, because you know now that he is capable of it.
There is a very very slight chance he is genuine and he has issues and he does genuinely want to change but even then, it won't happen in the short term. It takes years and years of therapy to change this kind of behaviour. And this depends on the person being open to it, genuinely wanting to change and accepting everything that they have done - which is very difficult for someone with anger problems to do.
The best thing you can do is move on with your life, keep contact only related to DD and do lots of reading, get some therapy for yourself, because there will be reasons that you attracted this/stayed in the relationship which you possibly aren't even aware of. Be kind to yourself :) And look after you and your DD. Take care.