Pat, we keep the actual passports in the room safe, but I always have copies of each with me.
I also have the passport control app on my iPhone which has the number. Picture of the passports are also saved on th phone, as well as an additional picture of my drivers license.
The person driving the car does of course have their license with them, and the rental car agreement.
I also have flight information if they need to know for immigration that I am leaving., or when and how I arrived...especially if it may have been via ferry or boat.