I didn't mean any of what happened, how do I explain this to her.
You don't. Instead of trying to convince a child that behavior her father -someone who loves you and has every reason in the world to cut you slack- has deemed so unacceptable as to remove her from your care is meaningless... It's time and past to work on your own self control so that you
never lash out at or around a child -or anyone else you don't intend to- ever again.
Speaking as both a parent and someone whose main issue was rage for many years. Rage takes more than 5 weeks to sort. Feeling sorry about what happened is different from having the self control, discipline, and emotional monitoring & regulation to be able to assert nothing like what happened will ever happen, again. That takes serious time, and serious work. Trying to convince people you've changed, when it's still your main issue, so you haven't even begun to change, yet? Is both a waste of time, and a broken promise, all nice and spring loaded aimed at the people you love.
Speaking purely as someone with explosive anger... Rage you didn't mean? Is the worst kind. It means your control is shot. Lashing out at/around anyone/anything that happens to be present whether it's due to stress cup, lack of sleep, panic attacks, insults real or imagined... Whatever the cause... When the result is a series of events that you never meant to have happen, don't agree or believe in, and have serious remorse over? Number 1 priority is learning to deal with your anger. Not seeking forgiveness. Forgiveness will come, or it won't, but it doesn't matter if your rage isn't handled, and you keep lashing out.
This is a good place to start
Dealing With Anger