Having a telephoto zoom can really help with getting candid and playful photos. While the lens is huge and heavy (not something you want to sling around your neck all day) it gives you enough distance that your kids (and most adults), will often forget that you are taking pictures.
When I am capturing my children with this lens, I think of myself as a wildlife photographer. I am there to observe and "preserve" the moment as it unfolds. I was about 50ft. away when our littlest decided to check in and make sure we were still there before venturing off to the edge of the field.