Hi…Well, you have conveyed maybe the source of some of this boy’s problems in your question: your girlfriend is single and working so the young child is in daycare. I am guessing since she probably has to support herself and her son, that she is working full time, and the boy is in full time child care.
What this means to me is that the young child does not have enough time with his mother and probably not enough time with his father either. I would start tomorrow morning with a new regime: the mom needs to spend at least 30 minutes a day of undivided attention with her son—if it has to be before work or after work, doesn’t matter. But he needs to know that this is his time, and no phone calls or preparation for dinner will interfere. When he starts getting more attention, and knows he can count on it, his behavior will improve.
And yes, I would talk with him about hitting as well. He knows its wrong. But just talk, no punishment. And, if there is to be discipline (ie teaching) it needs to happen on the spot—the day care providers need to talk with him and sit quietly with him for a bit.
By the way, research shows that boys do worse than girls in day care over 20 hours a week. Whatever time off she can take, I would take it and make special time for him as much as you can. He is still very young—and in a few years, he really won’t need so much time with his mother as he needs now.