I've no idea if the woman was right to tell your son off. Nor have you - and asking anonymous people on the internet - who weren't there - is going to bring no further clarity.
This last fact - which is glaringly obvious - suggests that you have another question in mind, and I suggest it is this one: "Was it cool for me to have started an argument with a random woman, in a supermarket car-park, in front of my son, through the window of the car I was driving?"
The answer to this is, clearly, "No."
Some reasons why: It would have been an opportunity to show your children how to de-escalate rather than create confrontations; you could have dealt with the issue privately, between you and your son, more effectively without including the other person; public spats are embarrassing; you were in control of a car, with a baby inside, and your son was on the pavement, outside, so (pragmatically) the actual physical locale wasn't the best/safest for this sort of discussion.
There are lots of others.
I'm guessing you were a bit stressed. It happens. Go and have a cup of tea and forget about it.
If you're like this a lot of the time - eeek! Arguing with people you don't know, about things that are not very serious (she wasn't importuning him/being violent/being dangerous,) is not cool. It suggests you wander around, seeing everything as a potential affront/insult to your status, and a power situation. It must be exhausting.