| Quote #1
All the while her thought was trying to justify her delight in the colours by merging them in her mystic religious joy. (1.1.36)
Dorothea is so caught up in her spiritual life that she feels guilty about her "delight" in earthly things, like horseback riding or the "colours" of her mother's emeralds. This "delight," though innocent, is something that she feels the need to "justify." So she tries to persuade herself that the "delight" she feels in looking at the emeralds is "mystic" – it will somehow help her soul get closer to God.
| Quote #2
The intensity of her religious disposition, the coercion it exercised over her life, was but one aspect of a nature altogether ardent, theoretic, and intellectually consequent. (1.3.13)
Dorothea's "religious disposition" has more to do with her spiritual life than with the doctrines of a particular religious sect. But her spirituality isn't always described as purely positive, it "exercise[s]" a "coercion […] over her life." In other words, her spiritual feelings coerce, or force her, to make decisions of which her intellect or common sense might not approve.
| Quote #3
Will was divided between the inclination to fall at the Saint's feet and kiss her robe, and the temptation to knock Naumann down while he was adjusting her arm. All this was impudence and desecration, and he repented that he had brought her. (2.22.32)
Many characters associate Dorothea with saints, angels, or the Virgin Mary, and Will is no exception. But Will doesn't associate her purely with the realm of the sacred. He's "divided" between his impression of her as something sacred (hence the desire "to fall at the Saint's feet"), and his sense of her as a physically beautiful woman who can inspire jealousy (hence his inclination to "knock Naumann down while he was adjusting her arm").