Why don't people take care of their dogs? My aunt, uncle, & cousins are driving me nuts!?

Actually, not brushing them and letting their nails grow to the point where they grow into the skin and it gets infected IS neglect. I feel so bad for those dogs, but they're lucky to have you. If I were you, I'd keep lecturing them until they listened, or report them if they didn't. Just because they're family doesn't mean they should be able to get away with neglecting their dogs.