i missed the saturday part in your write up. But taking the kids to the park for torah study would be something very observant jews might do. Go to temple in the morning and then walk to the park to study. Sure. But if the kids were playing in the park, not very observant. So the "we don't turn on lights" and such is off.

It's also possible that they are kind of observant but dad let's the kids play. Being Jewish really is a choose your own adventure kind of religion.