D Trad, I don't think what you did was wrong. Parents instincts...

D Trad, I don't think what you did was wrong. Parents instincts are to protect, and when analysed you did just that.
This is my view towards smacking - it is a kinder alternative consequence. The consequence had your child stayed in that car, or thought it was OK to do again had you not disciplined her, may have been to accidentally loosen the hand brake and end up in a crash.
The consequence of letting a child play with matches is a house burnt down and injury or even death. The consequence of a child running into the road could be injury or death and so on and so on...
A three year old doesn't understand gravity, or the likelihood of a house going up in smoke, and anyone who thinks you can reason with a child at that age is missing the point - they are not interested, they think it's really boring, they want to get on with playing. A quick smack is a kinder and swift alternative consequence, bedded into the memory, to make sure they never do it again. You're not asking them to understand gravity or physics - they've had a smack and move on.
Incidentally my definition of a smack is with an open hand on the legs or bottom. If your own hand hurts you most likely hit too hard - that is your barometer.
What I think is not fashionable, but I have three primary school age children who are lovely. They all got smacks every now and again in scenarios such as above, normal everyday scenarios for curious and fun children. Sometimes they got a little smack for being naughty - they are pushing their boundaries. They are all well adjusted popular high achievers.
Incidentally, my husband and I had children before any of our friends and we had no idea what we were doing. However, we did a pact that we wouldn't read any books, and we would just do as our parents did, after all we both thought the other was lovely enought to marry, so the parents must have done a good job.
I don't understand why many of my peers decide to parent differently to their parents.
Anyway, enough from me.....