C.,
Other than the whole time out idea, try what my brother does. My brother would tie, at the wrist, leg or waist, whatever worked, my niece and nephew together and make them do everything, except potty, together until they could apologize and get along. Usually took about 30 minutes.
Another approach I have done with my three boys, is I make them sit on the floor Indian style, facing each other. If I hear the blame game, they have to hold hands. If they continue to argue, they have to touch foreheads. If it doesn't stop there, then they have to kiss. I have pictures of this one to prove the point to them. Now, all I have to do is ask, "Is there a problem I need to get involved in?" Obviously, NO, and they work it out themselves. I have been doing this for about 5 years now with my boys.
Something else I do to them, I make them stand in a corner, and hold there arms straight out. If their arms are tired, they can't throw nor hit. Eventually, they realize this is painful and stop if you "threaten" the corner.
Another thing my cousin used to do to her kids, was to give them exercises to do. If they had energy to fight, they had energy to excercise. This may be young for your kids, but at 4, he will understand.
I don't know if this helped you at all, but I thought I would give some suggestions outside of the "time out, separation anxiety" issues. Good Luck!
Mother of 3 boys, 18, 15 and 10