homes, especially when that parent is a woman. I think your observation isn't atypical of many women. Moms are nuturing, loving, and an easy place to fall when a kid is down or struggling (we hope). Dads can function in this role as well, but are more likely to do what you did with your son, ie allow him to lose. What the mom didn't recognize is that you're at the park playing with your son. This is a huge predictor of success for a child--an involved father.
I have no idea if this mom was a single parent. I think she was exercising a momma bear reflex. When my wife does this, I don't criticize her too much, but I modulate it by beating my kid then tell him that he's getting better by practicing every day.