In Mansfield Park, why was Mrs. Norris so horrible to Fanny, when she was so quick to take her in at the beginning of the story?
The division of gratifying sensations ought not, in strict justice, to have been equal; for Sir Thomas was fully resolved to be the real and consistent patron of the selected child, and Mrs. Norris had not the least intention of being at any expense whatever in her maintenance. ... Under this infatuating principle [of extreme frugality], ... it was impossible for her to aim at more than the credit of projecting and arranging so expensive a charity; though perhaps she might so little know herself as to walk home to the Parsonage ... in the happy belief of being the most liberal-minded sister and aunt in the world.
Ah, interesting question. The answer to it requires careful attention to the text and careful attention to differences between our contemporary mores and those of Austen's time: Mansfield Park was published in 1814. One custom to pay attention to is that of the interdependence of families. It was not uncommon for wealthy families to assist poorer relatives with raising their children. [It was also not uncommon for wealthy relatives to let others sink in their own poverty as Thackeray's earlier novel, Vanity Fair, so well illustrates.]
The text relevant to Mrs. Norris's attitude is quoted above. In it, the narrator, speaking in Austen's ironical voice, is saying that Mrs. Norris is enthusiastic about her idea to bring one of the Price children to live at Mansfield Park Manor. Recall that Mrs. Norris lives in the parsonage located elsewhere in Mansfield Park. Mansfield Park Manor is Sir Thomas's home; Mrs. Norris is only a visitor there. In essence, Mrs. Norris is saying: "Hey! I have a great idea! Let's bring the eldest daughter here for you to raise and you to educate and you to feed and you to clothe, and I'll say what a wonderful thing I did by having my brilliant idea!"
Note she carefully uses plural and indefinite pronouns--carefully excluding herself from the consideration of expenses--when she explains how the cost of raising one more girl would be worth the sacrifice and hardly worth mentioning:
The trouble and expense of it to them would be nothing, compared with the benevolence of the action.
Give a girl an education, and introduce her properly into the world, and ten to one but she has the means of settling well, without farther expense to anybody.
The narrator makes it clear that Mrs. Norris's plan when, as you say, "she was quick to take [Fanny] in," was that the Bertrams take her in and she get the credit for it. With this in mind, it will be easier to understand Mrs. Norris's subsequent calloused behavior toward Fanny.
Another cultural point is that it was perfectly acceptable socially (though not morally or ethically) to treat wards, children taken in to the home, as "poor relations" who receive lesser accommodations and privileges. It is in this realm that Mrs. Norris's treatment of Fanny lies. [Why the Bertarams were silent and tolerant of Mrs. Norris's treatment of Fanny is another question altogether.] Thus we see that the answer to Mrs. Norris's behavior is that she was quick for the Bertrams to take Fanny in and that she was of the opinion that Fanny was inferior as an impoverished, rescued ward and thus deserving of inferior treatment.