The above was identified as a Red Bug (but looks like a Briggs and Stratton Flyer or Smith Flyer to me) based on the shifter lever and fuel tank, and is realistically the same as several other brand buggys, powered by a Motor Wheel, and look like a lot of fun. The top photo is the same company cart, but earlier and with electric power. The batteries are in the box on the back, and that is why the kids are looking like they can't find where to put the fuel
The fuel company product in the tank is "Whoo Pep"
from David's great vintage car photo blog http://theoldmotor.com/ where you can just look at the photos, or read about the history behind them too