Well, whether you allow him to see her or not or go down the contact centre route or whatever just be aware that his mindset has not changed - whatever allowed him to think, even for a second, that it was acceptable to hit you, is still down there.
Remember what I said, quite early on in the thread? He WILL promise counselling. He WILL promise to try, to take it slow, to change, that it will be different, that he regrets what he has done. It's a script - they all do it. Remember you said you didn't think he would react that way, you thought he would be angry. Please try not to hang on to this as false hope, either because you're grateful or surprised that he isn't angry, or because you're hoping that he's serious about it.
Do not forget that the first thing he did when he had a chance to contact you after the incident was not to beg for forgiveness or tell you how sorry he was or how much he regretted it, it was not to thank you for the wake up call or express how wrong what he did was, no, the first thing that he said to you (and he must have had time to stew on this and reflect, remember) was that he forgave you for calling the police on him.
Which means that he thinks he was more in the right than you were. Which means that no matter what counselling he goes to, anger management, whatever, it's not going to change those underlying beliefs that he has. The ONLY hope of rehabilitation for someone with an abuser's mindset is a dedicated abuser programme, and even those have a fairly low success rate.
What usually happens in these situations is that the abuser promises the world on a stick in terms of counselling and changing and everything turning out alright. Because you have a totally normal sense of grief at the relationship ending (happens even if you were unhappy in the relationship) and the sense of loss of those dreams and hopes and aspirations you had for the relationship, (everyone gets this) - what he's now promising feeds into all of that, because he's saying exactly what you're feeling/wanting, it's easy to see a connection that isn't really there. Although it's very difficult to accept this, it's all words. If your relationship was going to be like that, it would have been like that always - the reason it has gone wrong is the underlying attitudes that he holds that make it acceptable in his mind to control and abuse you. It's not something they do out of spite :( it's genuinely how they think relationships work, not an equal partnership, but a power struggle. You will never change that no matter how much counselling and talking and persuading you do, because you're coming at it from totally different sides. Imagine two people standing with a rope, where one of them is trying to tie it to something, and the other is trying to have a tug of war. And whatever they say to each other, each is convinced that the other is totally on their page, the person tying can't understand why the rope keeps getting pulled out of their hand, and the tug of war person can't understand why the other person isn't putting enough effort in, or why they're trying to cheat.