Hi OP I've been in a similar situation to you. I broke up with him but he acknowledged that he'd done wrong, showed me change, etc (although he never said it was abuse, but at that time I didn't recognise it as abuse either). I allowed him back and it was a matter of weeks before he started reverting back to old ways, although this time he was sneakier and more subtle about it. He tried to make me believe I was crazy and paranoid for thinking he was still being controlling. I broke up with him again 5 weeks ago today and quite honestly you couldn't pay me a million quid to go back. I have a young daughter and I refuse to teach her that any form of abusive behaviour is acceptable.
That being said, if you really feel he wants to change then there are options. Don't fall for the "I've changed" line because these abusive behaviours are extremely ingrained, and whilst some of these behaviours are deliberate, there are some which are just a knee-jerk reaction to situations. In order for a person to rid themselves of unhealthy behaviours, they need to replace then with healthy behaviours, and that takes some extensive therapy and a large amount of determination on his part. If he is serious about trying to change then there are a few perpetrator courses for abusers. If I were you I would insist he finishes a course before you even think about anything further. Then he should start a course of therapy with a therapist who specializes in abusers. They need to be specialised in order to know what to look out for with regards to manipulation. There have been cases where a therapist is taken in by an abuser and ends up reassuring him that he's done nothing wrong and its all the spouses fault, as the situation has been manipulated by the abuser. Bare in mind through all this that the statistics show only a 6% success rate where an abusive person who goes to therapy actually changes. That's only 6% of the small percentage who actually attend. I just want you to know just how few abusers actually change so that you don't get your hopes up.
And in answer to on of your questions: No level of abuse is ok. Either he becomes one of that 6% or he takes a hike would be my advice.
Well actually my advice would be to leave well enough alone. But if you're set on giving him another shot, don't go about it all willy nilly, ask him to get some therapy and put himself on an abusers course before you start considering anything else.
Good luck OP