It's not necessary to add your wife as a second driver with Avis/Budget. Per their terms, spouses are automatically included as an authorized driver on the rental. They do not need to be explicitly added to the rental contract.

https://www.budget.com/en/help/usa-f...-driver-policy

Who Can Drive My Rental Car?

If your additional drivers meet any of the following requirements, then they are pre-authorized to be an additional driver for a rental car.

• They are the renter’s fellow employee or employer AND the car is being rented under a business account.
  
• They are the renter’s spouse or domestic partner.
  
• They are the companion driver for a renter with a disability who has filled out the non-licensed renter form.
  

No fee applies to additional drivers in the categories above, and they don’t have to fill out extra paperwork to drive the rental car.