Sounds like my recent portrait session. I did a session with young parents, two kids. Baby was great - amazement to the parents. Their 4 year old did not want to participate. He decided he didn't want pictures taken.
Having no kids of my own, I'm clueless so my girlfriend who was acting as a helper and the parents tried their best. Nothing really worked. His mind was set! NO PICTURES! However, one of the best images was actually from this reluctant kid. The father decided he'll play a game of chase with this child. Within 30 seconds, he forgot all about the camera and started to play. I stood back and used telephoto to get some action shots. In the end, they have an image of their child paying with his dad and playing his favorite game, chase-the-dad.
I think, when child is involved, anything is possible and having an open mind about what photographs to take is an asset. Sure, they didn't get many everybody-sitting-and-smiling photo of him but they did get something they'd love and keep.
Strangely, last year, he was a happy kid who smiled on que.... I learned later, he didn't get his nap that day. Oh well.