This parallels Satsuki's coming of age subplot (she's ten and like anyone that age she is self-conscious about believing in Santa, or in this case Totoro). Throughout, you see them subtly (almost too subtly at times) change from completely carefree to terrified with each scene involving the mother.
The Mother: I think this movie is entirely about the mother. This is why an accurate dubbed version is nearly impossible (like any little girl, Mei mispronounces a lot of words). On top of that, according to Helen McCarthy and other Miyazaki experts, the name "Totoro" is little Mei's mispronunciation of the Japanese transliteration of the English word "troll" ("tororo," which the Japanese would pronounce like "tololo" because they do not distinguish between r's and l's).
Secondly, Mei and Satsuki are really into Western fairy tales (the are brief glimpses of Japanese translations of The Three Billy Goats Gruff and other stories, along with Mei inadvertently re-enacting scenes from Alice in Wonderland and Chronicles of Narnia). Americans: First of all, the house the girls move into is rather European in design (with doorknobs, and an attic, and a front porch) despite the Japanese style bath and occasional sliding door. Although some people who watch this movie wonder where the Americans are (this is post-WWII Japan, after all) and why so little screen time is spent on the girls' mother, but that may be partly due to the dubbing. This movie, set in Japan in the early fifties, is director Miyazaki's tribute to his mother (who suffered from tuberculosis, just like Satsuki and Mei's mother), his childhood home, and childhood innocence.