Is it inappropriate to ask boarders to leave an emergency contact?

When booking on Rover, clients are to fill out the emergency contact and vet contact section. Always check it's completed before accepting the dog in your home. If it is not filled out, you need to ask them directly to update it, so you and ROVER has an access to the info.

No, it is completely appropriate. At the M&G, I give owners my Dog Info Sheet, which asks for basic as well as behavioral information. In the basic section, I ask for Emergency Contact information that I specify as NOT being the person they are traveling with. They return the completed sheet when they drop off the dog.

As a business owner, you can ask and require anything you'd like to make the dog's stay safe for all concerned.

It’s appropriate to discuss and ask. Their reaction will likely reflect how they feel about your communication. (Ideally, discuss this before the booking, in a friendly tone, coming from a place of preparedness) Regarding Vet approval, You can ask the parent if they will provide credit card information to their vet along with written authorization that they can discuss with you as the pet sitter if the dog needs to be brought in for care.