How does "The Artist of the Beautiful" resist aspects of nineteenth-century daily life?

I would not say that "The Artist of the Beautiful" resists aspects of "daily life" so much as it depicts a situation that would not be possible in the early nineteenth century.
The invention that Owen Warland produces is a mechanical device capable of flight, an artificial butterfly. Other tales by Hawthorne, such as "The Birthmark" and "Rappiccini's Daughter," similarly show inventions that could be the product of either futuristic science or the supernatural. Earlier in the nineteenth century, two other writers explored similar themes: Mary Shelley (in Frankenstein) and E. T. A. Hoffmann (particularly in his story "The Sandman," in which a man creates a female mechanical doll). So Hawthorne's fiction is part of this early science fiction movement in literature. The technology actually available in his own time wouldn't support the wonders he describes.
If aspects of daily living are given short shrift in Hawthorne's story, this is also something typical of early nineteenth-century fiction, at least in comparison with the more realistic and naturalistic works written from the latter part of the century up through our own time. The mundane details of life weren't chronicled carefully by earlier writers. In "The Artist of the Beautiful," the focus instead is on the inner lives of people—especially Owen, as he agonizes over his work and his feelings for Annie. He is a dreamer, and the whole story is dreamlike, though perhaps not as intensely so as other Hawthorne tales (such as the two mentioned above) and those of Edgar Allan Poe. The physical setting is less important than the mental atmosphere Hawthorne creates, in which a man is struggling with his inner demons.