What does Anne mean when she mentions that Peter has two anne's before him?

Answer 1

Anne came to see herself as "two Annes" - the outward one everyone saw: Boisterous, chatty, excitable, somewhat argumentative. The "other" Anne was quiet, reflective, and felt things very deeply. The "other" Anne was also very vulnerable - not in control of the situation, and that is why Anne feared the "other" Anne and let her come to the surface so rarely.

Answer 2

When Anne Frank mentions that Peter has two Anne's before him, she is referring to herself and her mother. She sees herself as one version of Anne, and her mother as another, and suggests that Peter now has to deal with the combination of the two.