I'm confused, too, about what Granny's actual situation is. Is she actually "refusing," or is she physically or emotionally unable (depression can effectively disable a person). But beyond those questions, I have a few thoughts;
I had no idea how challenging my grandmother's physical experience probably was until I got to be a granny myself. It can be more exhausting and uncomfortable than a young, healthy person can imagine.
My house isn't as clean as it was when I was younger for several reasons. I can't see the dirt as well. Dust bunnies in corners don't hold loud parties, so I let them be until I have the energy for a major cleaning a few times a year. Vacuuming everything in my small house can take me up to three days in several short sessions because of physical pain. It's a pretty daunting job.
Cleanliness isn't necessarily all it's cracked up to be. Recent research reveals that, not only are many modern cleaning products, disinfectants and air "fresheners" actually toxic and hazardous to health, but also that children raised in very clean environments have confused, over-reactive immune systems, resulting in a higher incidence of asthma and possibly other allergies. Their systems have never learned to differentiate effectively between "friend" and "foe."
When you think about it, dirt is pretty clean stuff. We do allow kids to play outside in the yard, the park, on surfaces and equipment lots of other kids and pets have occupied. Why should dirt in the house be treated as some special horror? If you ask me, modern moms have been manipulated by advertising into believing they have to have immaculate homes to be a worthy wives and mothers.
Now, this is not to condone grimy, greasy, or stinky bathroom and kitchen surfaces, soiled or sour linens, etc. Perhaps my house is a bit eclectically cluttered, but I would not want to put my grandson at risk of getting his hands on infective or otherwise unsafe materials.
If Grandma has wisdom, character and love to offer her grandkids, I would look for a solution. Can you help her straighten up when you take the kids over? Can you relax your standards? It almost sounds as if you'd rather not bother, so I wonder if there is some other issue at work here.