Will your ex-girlfriend ever be with you again if you hit her once and told her family but you apologized?

You probably blew it. The fact that you were unable to control yourself and lashed out violently reflects poorly on you and bodes ill for your relationship. You might never raise a finger toward her again, but if I were her, I wouldn't take the risk of finding out. It's a difficult pill to swallow when we realize how badly we scewed up. It took guts to apologize to her family and I am sure you do feel badly. However, as the poster above said you blew it. There is so much abuse going on towards women (and even women abusing men) that there is zero tolerance for this sort of behavior and the person that was abused by that slap can't afford to take a risk of the same person doing it to them again. You should know that when you are angry you need to get away from that person and walk it off or go hit a punching bag, not someone's face.