Just for starters, let's say (as your message suggests) an image at 8 feet, 85mm, f2.8. With a child "running around." The depth of field would be 5-1/4 inches (13 cm).
So you have this really minimal depth of field, combined with a shutter speed of 1/125th second, and a target that's "running around," and a camera that's trying its damnedest to keep up with it. That's a formula for failure. (Not to even mention release priority?)
Think first about shutter speed, then a smaller aperture to get some focus breathing room --- both of which will likely require a much higher ISO (a factor of 4?) and/or probably flash.