Dear Done with the dog,
Is it too late to fake a pet allergy? Just kidding, don't lie. There's no reason that inviting your friend over should mean dealing with her animal chez toi. I know many pet owners consider their pets part of the family, but you're perfectly within your rights to implement a people-only policy in your own space.
There's really nothing to do besides pure honesty. Next time you invite her over you need to nicely clarify that the dog isn't welcome. Don't bring up past visits or blame the dog for bad behavior, just say: "come over for dinner next week and please leave your pooch at home."
If, for some reason, she goes against your wishes and brings her dog anyway then you shouldn't let her inside. Really. I know that sounds harsh but it's is SO disrespectful to ignore the wishes of your host and it sounds like she could use a lesson in boundaries. You will be standing up for pet-hair haters everywhere.