Lady (stranger) shouting at my 8 year old son

Am I in the wrong for shouting at a lady for shouting at my son???

I took my son 8 and my granddaughter 4 on a bike ride , it's a joint walkway a bike path , my son has only ride it once before and that was a year ago, on our way back to the car my son come out of his lane to get closer to a viewpoint to look at the ducks on the water in doing so a lady in her mid fifties who was walking her fluffy dog had to stop as he cut across bearing in mind I'm on foot so a bit further back so she didn't know I was his mum, she started shouting at him saying look where your going , what are you doing etc, so I shouted to say don't shout at him I'm his mum I can tell him off your a stranger you shouldn't shout at other people's children, she says well keep your child under control to which point I hit the roof at her, I could go into a lot more detail but my point is, is it ok for a stranger to shout at your child??? Am I in the wrong?