My son likes to watch a specific YouTube video in the car sometimes, and he always touches the screen and stops the video. Is there any way to prevent this while keeping the screen on?
You may want to install the Touch blocking App such as Touch Blocker.
How this works?
Touch Blocker prevents unintentional touch interaction with the touch screen of your device by blocking touch input. When you disable touch input while watching a movie you don't have to worry not to skip scenes by accidentally touching the screen.
So, as soon as you begin to watch YouTube video, Enable touch blocker: Just need to touch notification icon to enable it.
And when you are done with Video watching, you can disable the touch blocking. The Touch Blocker app which is mentioned in above link has many different ways of unblocking the touch, such as pressing Volume Up button on the device.