Her name is in the title of the book, so Mrs. Frankweiler must be a pretty important character, right? Right. As the narrator of the story, Mrs. Frankweiler tells us all about Claudia and Jamie's adventures—but she also teaches us a little about herself.
No, you haven't stumbled upon the analysis for Wormtail. If Claudia is constantly looking for secrets (which she is) then Mrs. Frankweiler is on the other end of that—she has plenty of secrets that she's kept over the years. After all, she's an old lady. Eighty-two years old, to be exact.
The fact that she keeps secrets is no secret. In fact, she tells Claudia and Jamie straight out:
"Secrets are safe, and they do much to make you different. On the inside where it counts. I won't actually be getting a secret from you; I'll be getting details. I'm a collector of all kinds of things besides art," I said, pointing to my files. (9.235)
Mrs. Frankweiler has one particularly big, honkin' secret: whether or not the angel statue was carved by Michelangelo. Even though the museum officials are all clambering to find out the truth, she refuses to hand over the documents. As Claudia puts it, "She would have shown her evidence if she really wanted a big price. She sold it for the fun of it. For excitement" (10.13).
That's right: it's fun having a secret, but not so fun if no one else knows that it's a secret. By selling the angel statue at an auction, she was flaunting her secret in front of the world, without giving them any of the juicy details. Pretty mischievous for an old lady, don't you think?
That's probably why she relates to Claudia and Jamie, who are also little troublemakers in their own way—you know, running away from home and all.
Most particularly, she and Claudia are like two peas in a pod. Both ladies, no matter the age, love having their own secrets and feeling special because of them. Mrs. Frankweiler totally gets what Claudia needs—even when Claudia herself doesn't quite know. That's the experience and wisdom that comes with age, we guess.
Even though she's kind of standoffish (at least at first) and lives all alone, Mrs. Frankweiler becomes exactly the kind of grandmotherly figure that Claudia and Jamie want to embrace. She may not be the usual milk-and-cookies kind of grandma, but she treats the kids the way they want to be treated—with respect and appreciation for their intelligence.
Instead of acting like they're just normal kids who have to go through the usual chores, schoolwork, and all that other drudgery, she listens to what they have to say and then strikes a deal with them, just like they're equals. She bargains with them to trade the secret of the angel for the secret of their runaway lifestyle:
Jamie's face broke into a huge grin. "Bribery!" he exclaimed. "You're going to bribe us. Hallelujah! Tell me. I'm ready. What's the deal?"
I laughed. "The deal is this: you give me the details of your running away, and I'll give you the sketch." (9.226-227)
Jamie is super psyched, clearly. He's being treated like an adult—illegal bribes and all.
Even though Mrs. Frankweiler is super good at keeping secrets (or at least collecting them), the kids pick up on one secret she doesn't tell them: that she doesn't have any kids or grandkids and wonders what it would be like to experience that. Instead of just writing her off as a means to the end (finding out the secret about Michelangelo), Claudia and Jamie feel like it's their duty to treat her as family, to give something back to her. In the car ride on the way back home, Jamie says,
"And that will be our secret that we won't even share with her. She'll be the only woman in the world to become a grandmother with never becoming a mother first." (10.28)
Don't forget, as the grandmother figure in the book, Mrs. Frankweiler is also connected with the children's grandfather, Saxonberg. At first, we think he's just her tax lawyer, but it's obvious that they've known each other for a very long time—after all, would you write that long of a letter to someone you didn't consider a friend? You could even say that she considers Saxonberg a really important part of her life, like a family member.
There's a sense that everything comes back to family in the end (even though it's what Claudia and Jamie are running away from). That's only made more clear when the kids decide to adopt Mrs. Frankweiler. It's like Claudia decided to escape her annoying family, but did it all the wrong way. She brought her little brother, adopted a new "grandmother," and inadvertently involved her grandfather.
You know what they say. Family first.