What do you think about me telling my mother she won't be able to visit us with her dog?
Why can't she visit with the dog?
They are destructive animal with fleas, they make holes in the house, I'm allergic to dogs
Even though it will make her life harder to board her dog, it is okay to have boundaries and not want the dog around. You will be happier to hang out with her without worrying about the dog.
I should just tell my mom to get rid of the dog altogether.
If you genuinely do not want the dog in your home, that is understandable. However, you should care about your mom and not go out of your way to make her feel uncomfortable.