Candid photos are the best. Formal settings and posed shots are the things of the past. They were a must in the early years of photography when people had to remain frozen in front of the camera for extended periods of time due to long exposure necessary for making a decent shot.
Kids were notoriously difficult to photograph (they still are) as they have trouble staying still and frankly don’t feel the need to suffer for the sake of preserving images of themselves. This is why there are some weird vintage pictures where the controlling mother is disguised as a chair.
The modern cameras are fast at capturing images in action. There is no need for prolonged posing.
Though family photographer still like to create arty images and can be good at making children pose for them.
If you want to replicate such achievements, you are guaranteed to fail.
Where you can beat a professional photographer is candid shots. Children feel more relaxed without pressure of a timed photo shoot and their true personalities shine.
Engage your kids in their favorite activities and keep your camera ready. You’ll get much more interesting shots than the cheesy smiles into the camera.