Unless you have exemplary camera holding technique or are shooting from a tripod, from 20 or 30 feet away using a 70-300 mm lens 1/80 or 1/100 won't be a fast enough shutter speed to ensure the control of camera shake blur, let alone child motion blur. At 20 feet away you would likely have the lens zoomed to about 200 mm and need closer to 1/200 for your shutter speed.
You need to know that depth-of-field produces a zone of sharp focus that is in a plane approximately parallel to the plane of the image sensor in your camera. Each lens will produce some amount of 'field curvature' that make the DoF less than parallel to the plane of the image sensor.
With sufficiently deep DoF, the zone of sharp focus is sufficiently deep enough to have all eyes in focus.
So using a DoF calculator, the total DoF a T3i with a 50 mm lens set to f/8, and point-of-focus (PoF) 10 feet from the camera will produce is 3.77 feet.
However, that total DoF is not evenly distributed in front of and behind the point of focus. The distribution is 41% in front and 59% behind the point of focus.
At f/11 the total DoF only increase 1.75 feet to 5.52 feet, and the DoF distribution gets more difficult to work with at 37% in front of, and 53% behind the PoF.