Ex-wife of an alcoholic here with a 20-year-old, very emotional daughter. She can escalate from 0 to 60 in 2 seconds. I can sympathize. It has taken me years to learn not to escalate right along with her. I'm not always successful.
In this situation I would tell her I'm sorry about my part in the fight including of course striking her. I would try to get into family counseling with her as soon as possible. Best of luck to you.