Either battery, simple battery, or family violence battery, it all depends on the level of injury to the child. However, there maybe several defenses to any charge against the parent as Georgia allows reasonable corporal punishment by parents of a minor child.
Actually, the provocation you describe (or even the use of profane language toward you) is an absolute defense to a Simple Battery in Ga. Note that I said simple battery, not Battery. A simple battery is an offensive touching while a battery is such a touching that leaves visible injury. So a slap on the face that does not leave a visible injury such as a bruise or a cut may be just a simple battery. If that slap was preceded by the use of foul language or threats of harm to you, then the slap may be entirely appropriate and not subject to criminal prosecution. Some years ago, I obtained a dismissal for a man charged with simple battery who slapped his 16 year old daughter after some choice words flew from her mouth during an argument. The man was arrested (since the police sometimes do not know the law of defenses) but the magistrate dismissed the charge at the preliminary hearing.