You were perfectly within your rights to defend it as your own business and none of hers.
However, when my sister decided to have a tantrum at about the same age, lying on the floor, kicking, crying and screaming, my father said, "If you want to cry, I'll give you something to cry about." After a brief spanking, which gave her a reason to cry, she calmed down and never had a tantrum again. When a tantrum is immediately treated with a quick spanking, a child soon learns that tantrums not only do not get them what they want, they get something they don't want.
I think that allowing tantrums, even though you do not let the child get their way, teaches them that they can be annoying to everyone and no one will stop them. It is more abusive to let them get away with it than to give them a spanking. And that is a couple of open-handed swats on the bum to get their attention, not a beating. The child quickly learns that they will not get what they want and that they get something they don't want, when having a tantrum.
Good behaviour needs positive reinforcement and bad behaviour needs a negative reaction.