I haven't really ever understood why some folks get so bent out of shape over whether a guinea pig is a rodent or it isn't. They're pets, most of us here love them, so I can't quite get my head around what it matters what their actual classification is. Rabbits are lagomorphs but they're still, in the scheme of things, kinda gross - they pee/poop all over (without training) and destroy things (without supervision). Rats are rodents but they make wonderfully sweet companions and people find them to be very rewarding pets. To me, it's never mattered what their official classification is and I can't quite understand why some folks try so hard to suggest they are more rabbit-like than rat-like when they just are what they are - sweet little animals that many of us share our lives with and find to be wonderfully rewarding companions, whatever they are "officially." I mean, really, if we're going to get into it, chinchillas are rodents, too, but they're arguably more sophisticated and much more exotic than a guinea pig ... Official scientific classification just doesn't seem terribly important when we're talking about an animal that we love and enjoy spending our lives with - what they are or aren't doesn't change their status as delightful companions.
As to the daycare, as others have suggested, no I don't think pets kept in sanitary conditions are going to have any impact on your mom's inspection.