@Shari175 I agree you could turn off instant book but it does impact your search ranking in Airbnb. When I read your listing I see pets allowed but I do not see the 1 dog limit in your house rules. I do not see where the guest booking would know there was a 1 dog limit?
I would add this to your house rules and in your property description so it is clear to guests.
For the guest that messaged you with the 3 dogs (I would ask what kind of dogs they are) 3 Chihuahua's are different than 3 Great Danes. If you are still uncomfortable I would ask the guest to cancel and offer a full refund vs you cancelling so it will not count against you.
Jorge