Quoting Kelly&Coralie:" First off, how does hitting him teach him not to hit? Redirection, positive reinforcement, rewards for good bahviour, ignoring the bad behaviour."
Hitting a child for hitting does not teach them anything. However with the other girl starting it, is this in day care? If so why have they not taken action against the other child? I would take it up with the teacher/ care provider and demand action be taken.
If this is on supervised visits where you and the other mom are present, talk to the other mom. Or dad if that is the case.
He is only fighting back for what she has done/is doing to him which I can understand and with that being the situation it makes it hard to punish because he thinks he is doing the right thing (especially when you "pop" him for that behavior). At 19 months they do not have a true concept of bad and good yet and are still learning. If he gets punished after the fact he will correlate it with him getting punished for no reason so that will not help the behavior at all either.