How does Anne Frank hurt her mother in Act 1, Scene 4? How do Anne's gifts to her mother and Peter show she has changed?

Anne hurt her mother when she refuses to let her stay with her after her nightmare and instead asks for her father.

Being in hiding is frightening for Anne. She often has nightmares. In this scene, Anne makes up a nightmare and everyone tries to soothe her. Her mother wants to stay with her, but she doesn’t let her mother stay. Anne and her mother have a rather strained relationship that didn’t get much better in the close proximity of the Secret Annex. 

MRS. FRANK. Poor darling. Try to sleep then. I'll sit right here beside you until you fall asleep. She brings a stool over, sitting there.

ANNE. You don't have to.

MRS. FRANK. But I'd like to stay with you. . . very much. Really.

ANNE. I'd rather you didn't (Act 1, Scene 4).

Anne adds insult to injury by asking for her father. It is bad enough that she doesn’t want her mother there, but the fact that she wants her father instead is very hurtful to her mother. Her mother doesn’t intend to be a bother for Anne, but they are always at odds just the same. Margot tells her mother this is just a phase girls go through where they prefer their fathers.

Anne explains to her father that she had a bad dream that the Nazis were coming for her. Mr. Frank tells Anne she hurt her mother by refusing her, and Anne realizes she was cruel.

MR. FRANK. You hurt her very much just now. She's crying.

She's in there crying.

ANNE. I can't help it. I only told the truth. I didn't want her here. . . Then, with sudden change. Oh, Pim, I was horrible, wasn't I? (Act 1, Scene 4) 

Although Anne might appear selfish, in Scene 5 the distribution of her presents shows she does think about others. There is no way to go out shopping, so Anne uses thoughtful planning and creativity to get everyone gifts. She carefully erases all the puzzles in a book of crosswords for Margot, for example, and gives her mother an I.O.U of ten hours of doing anything she said. That gift in particular demonstrates Anne knew she could be trying to her mother and is making a lighthearted attempt to make up.