You might very well be crazy but that has no bearing on the matter. You felt it was your duty to inform the other mother about conditions you felt were unsafe. It was the other mother’s perogative to either thank you or ignore you. You have no further duty, nor do you have any basis to assume that your are a “better mother” that she. Frankly, when I was a kid no one ever thought to wear a helmet while bike riding and I don’t recall any issue of common head trauma.
To all: I strongly recommend reading “Free Range Kids” by Lenore Skenazy