Dear Student,
"But remember -remember a firm hand" was told by Mrs. Fitzgerald to Mrs. Pearson. As Mrs. Fitzgerald observed that Mrs. Pearson's family members were miserable about her changed personality and things were gone far enough from what they had predicted, she suggested that they must change into their original personalities. After they got their own personalities back, Mrs Fitzgerald asked Mrs. Pearson not to go soft on her children and husband again. She told her that Mrs. Pearson should let them do the things that she wants them to do but her children and husband don't do. She expressed her wish to play rummy with family. Mrs. Fitzgerald wanted Mrs. Pearson to be strict enough to be treated like the mistress of the house and get respected by her family. This is when Mrs. Fitzgerald said the above line.
Regards