If I request 2 different dog walkers for the same time to make sure I get a dog walker, is there a way to guarantee that I don't accidentally book 2 walkers for the same time?

There are no guarantees in life but if you created 2 booking requests you should only accept the request with the walker you feel the most comfortable with after the meet and greet

Rover needs to allow the dog owner the option to cancel/delete a request. For some reason they do not allow that. Their website and app are inferior & need a lot of help.

The quick and dirty answer is - YES.

You have to accept the booking from the walker before it is set in stone.. However, I am not familiar with how the booking system works and if you can make multiple requests. Like Walt says, only accept the request with the walker you feel the most comfortable with after the meet and greet.