Is cursing in front of your children child abuse?

I don't think so, only if any sort of abuse happens to the child.

It might be traumatizing for the kid to witness it, and I'm sure it's likely for the cops to be called. If there's punches being thrown & very strong language, its probably very bad for the child. I would suggest going into a separate room & fighting if necessary or not fight at all. Spending a little time away from each other could help. Time is all you need. If the child is old enough, explain why you and the other person are arguing. Over the phone fighting is better, and safer. I wish the best of luck!