Get a couple of flashes with cheap radio triggers and point them at the ceiling/corners of the room. Adjust their power until you get about f/11. You'll have pretty uniform and natural-looking light all across the room, so just chase the kid and push the button whenever. If shooting B&W, consider a green gel for the flash; it can improve skin tones in some cases. A red filter will make people look like white marble, if that's what you want.

If you light only the ceiling, the light can be a bit too directional and cause shadows under eyes/chins. I find it best to get about 3/4 of the light (depending on how bright your walls/floors are) on the ceiling and the rest on opposing walls, which will give you a nice ambient fill while still providing very good shading/rendering from subject shape.