In act 2, scene 2 of "The Diary of Anne Frank," Anne has another date with Peter. Anne apparently hasn't asked permission from her mother to visit with him again because Mrs. Frank asks, "Anne, dear, you're not going in again tonight to see Peter?" She must feel that she is losing control of her daughter because when Anne says that she will be visiting him again, Mrs. Frank asks if she will leave the door open while she is in there. Anne's reply is that her mother is acting like Mrs. Van Daan. Mrs. Frank politely says that she isn't implying that anything bad is going on, but not keeping the door open could invite "unpleasant" criticism from Mrs. Van Daan. Anne shuts down her mother's arguments by basically saying that she will do whatever she wants. Consequently, Mrs. Frank retreats quietly.
It can be inferred from the scene between Anne and her mother that Mrs. Frank wants Anne to be friends with Peter, but she doesn't want Anne to get into any trouble with him. She doesn't want to suggest that Anne will get into trouble, but she also wants to control the situation between her daughter and Peter a little bit. Mrs. Frank and Anne don't get along very well as it is, so it seems as though Mrs. Frank also doesn't want to push her daughter too far and cause more of a conflict than there already is between them. Furthermore, since Anne is her "baby," Mrs. Frank probably feels inclined to protect her daughter from any heartbreak from dating too early. Whatever the case may be, it is natural for Mrs. Frank to have motherly concerns about her youngest daughter visiting an older boy as often as she does.