Mrs Norris do so want to be important (e.g. she picks up Fanny and "regaled in the credit of being foremost to welcome her, and in the importance of leading her in to the others, and recommending her to their kindness" in Ch. 2) and having lowly Fanny around to trample on probably makes her feel more important. No Fanny, no one to trample on; Mrs Norris is herself at the bottom of society.

I was also thinking that Mrs Norris treats Fanny the way she does because she (La Norris) is still mad at Fanny's mother. Frances Ward married "to disoblige her family" and clearly Mrs Norris still resents her choice and now she treats poor Fanny as if it was somehow her fault. She treats Fanny the way she would have treated her mother if she was around - she is not, so Fanny has to take the blame.