Hi Lana -
Check out the link Deb posted to review Rover's insurance policies. Any questions about the insurance coverage should be directed to Rover's customer service. If you have any specific concerns about your dog while they are in the care of a sitter, be sure to address those concerns with any potential sitters prior to booking the stay.
Holding meet and greets are critical, especially if you're concerned about conflict. Both you and the sitter should be comfortable with how the dogs behave together, and the sitter should be providing sufficient supervision. They should also have a way to safely separate the dogs when supervision isn't possible and in case of conflict during the stay. If you're really worried about conflict, hiring a travel sitter to come to your home, or booking with a boarder who doesn't have other pets may be your best option. Not all dogs enjoy sharing their space with other pets.
Sitters should have safety nets in place to prevent the loss of a dog in their care. Personally, I have a gate on my porch that I can leave shut so when I open the front door I don't have to worry about a dog slipping by me when I'm coming and going. If my hands are full, like carrying something to or from the car, I'll use crates, tethers, or interior doors to keep dogs safe while I enter and exit. I don't let dogs out unsupervised. I'm careful to make sure guest dogs' collar or harness are secure. Early on I had a guest slip her collar while out on a run (thankfully she didn't go anywhere), and now I'm extra careful. If I don't feel comfortable using the equipment provided, I have extra collars and harnesses I can use.