You're not an overprotective parent, just...cautious—which is why your kids still write with safety pencils and circles of paper even though they're nearly in college. And how are you going to teach them to drive? Thos things are automotive deathtraps! The Humanix iSAVE-SC1 might be a good start.
The Humanix iSAVE-SC1 is a pillow-protected runabout resembling a three-wheeled golf cart. Its electric motor only outputs enough juice to get the cart up 30mph but for a vehicle built with—and only—safety in mind, that's plenty quick. Its exterior body panels have been replaced with inflatable bladders constructed from tent fabric so that, even if you do manage to catch a pedestrian unawares, the ensuing contact should do little damage (assuming you just hit him and don't run him over).