If this mother wouldn’t give her child a smack because she ran out into a busy road, then she’s not much of a mother. She loves her ideals more than she loves her child. Actions speak louder than words.
When I ride bikes with my kids, especially when they were younger, I was an absolute tyrant. In no uncertain terms, I am the absolute law. “If I say STOP, I want skid marks. I will do whatever it takes to keep you safe, including knocking you off your bike.”
When my son was about 5 or 6, we were riding on a side street and he began to drift out with a car coming, (not too close) I grabbed the scruff of his shirt and yanked him off his bike as I was riding. Guess what? He got the message.