Eleanor, I was not perpetually anxious either - but I early on decided that the safety of this being I had brought into the world was mine. So I taught him how to cope with various things, eg re crossing the road: to use the local zebra crossing, look both ways etc, did it with him numerous times from babyhood onwards, of course, then watched him do it by himself and them let him set sail doing it himself etc. And he was taught to do things according to his age and understanding, not when he was not old or experienced enough to understand implications. Has it created a neurotic adult? - no way. It has created a very confidant, capable adult. I believe your job as a parent is to work yourself out of a job!! But to do it in a safe and responsible way.
But all this comes throughout childhood as the chid is led safely to adulthood - it is not at ages 2 and 3
Funny you should say that. My eldest son must have been about three when I went running to rescue him from a swing. I stopped myself because that was when I realised that I couldn't forever protect him.
My middle son was about four when he used to run off to The Kampong to play with his Chinese friends, and I didn't stop him from doing that.
My youngest son was just a baby when I allowed his Amah to take him home with her for Chinese New Year overnight.
No, I didn't much like any of it. But you have to start somewhere, and then hope for the best from all people.
Sadly, Madeleine was abducted by a s..m bag of some kind.