Hi A.,
I have a similar situation with a friend that doesn't clean. There are visible chunks everywhere (Food, dirt, dog hair, you name it.) She only lives 30 minutes away and I haven't been to her house in over a year. She also has a dog that has to be in it's crate or it goes on the floor. I understand how you are feeling.
My solution was to meet her places. I know that you are limited with your friend not having a car. Can you all fit in your car? I would try to meet at a zoo, a children's museum, park or playland (which can be just as gross! :). I haven't had to have that confrontation because meeting places works better for both of us since I work 1st shift and she works 2nd.
Good luck. I can't really say to be upfront because I don't have it in me to do it. If it came down to it, I guess I would say that you are questioning pet allergies in one of the kids and you would prefer to steer clear of the dander.
C.