The more your child has to go to the bathroom, the farther you will be from a potty.
When on the road, your child's need to go potty varies inversely with the speed of the driver immediately in front of you.
When searching for the nearest public bathroom, the most direct route to the potty will be blocked either by a gaggle of teenagers or somebody on crutches.
The first public bathroom you find will be filthy.
The second public bathroom you find you will only be able to use once at best, because the sound of the flushing toilet will be audible in the next time zone and will so thoroughly freak out your child that the third, fourth, fifth and sixth public bathrooms you find will be deemed unacceptable if they look anything like the one with the big scary loud toilet.
If the big scary loud toilet in the next stall over flushes before your child has done their business, they will be freaked out and refuse to use the toilet they're at. Proceed directly to the seventh available toilet as alluded to above.
Auto-flush electric eye toilets will either be terrifying and unusable, or your child will delight in repeatedly setting off the sensor and completely forget the business at hand until such time as the toilet overflows.
If the toilet in the next stall over is being used by somebody whose most recent meal appears to have been burritos and Utica Club, again there will be a freaking out and a potty refusal.
If all else fails and you pull over to make a dash for the nearest tree, within one minute a police officer will arrive at the scene to investigate the situation. Meanwhile, seventeen meth dealers, half the Gambino family, and one recently-indicted member of the state legislature will insouciantly blaze by in the opposite direction.