Parenting observed

On the local MAX train a few weeks ago, I saw a family of three standing together, a kid, maybe 8 or 9 years old, his young mom, and his middle-aged grandma. (Guessing about genders and relationships here.) They all looked relaxed and joked around together. I noticed how settled the kid was, not frenetic like most kids I see on the MAX. He was wearing a backwards baseball cap, and his mom gently stroked the hair that was poking out over the strap. He looked up at her with pure open love, like a cat. That family is doing something right.

The other day at the optician, I saw a young mom with three little girls, aged something like 3, 4, and 5. The girls were all over the place like ferrets, and their mom was constantly snapping at them and grabbing them by the arm. She said to the air, "I don't know what to do with these girls to make them behave and be respectful. I've done everything, taken parenting classes, everything but whup them." The two older ones started drawing with the crayons available at a little child's table, and the oldest said over and over, "I'm a terrible drawer. I'm a terrible drawer." I wanted so badly to say something, but I didn't see a way to intervene. I tried to catch the eye of the youngest and smile at her, but there was no spark of contact there. I'm sure the harried mom of three with (it appeared) very limited resources is doing her best, but her best is failing those kids miserably.

ETA: Everyone in these families appeared to be white.