Everything ties up neatly at the end of From the Mixed Up Files of Mrs. Basil E. Frankweiler, kind of like a perfectly wrapped gift. The secret of the angel is resolved, the kids go back to their parents willingly, and everyone is considered family, even Mrs. Frankweiler. Talk about a heartwarming ending.
There's more to the wrap-up than just that, though. The ending comes with the big reveal about the angel statue, which makes Claudia feel like she's going back home "different." But the children and Mrs. Frankweiler are changed because of their encounter; they become "different" not just because of Angel, but because they've met each other and have gained a new member of the family—one that they've chosen, who's not just imposed upon them (like Kevin the brat is).
The secret of the angel sticks with them in the end, but they also reflect on each other. In the car on the way home, Claudia and Jamie decide that they're going to adopt Mrs. Frankweiler as a grandmother, because they've forged such a deep connection with her that they see her as family. And at the end, Mrs. Frankweiler muses: "I wonder if Claudia and Jamie will come visit me again" (10.33).
In a kind of mixed-up way, the story turns from being a good old-fashioned art mystery to one that examines human relationships and what it really means to be family. In the end, they're all thinking about that—Mrs. Frankweiler even considers what her relationship to Saxonberg is if she's considered the Kinkaid children's grandmother. We don't even see the moment when they reach home again and reunite with their other family members—we're left with the moment when they've chosen someone to be their grandmother.
Maybe, in the end, family isn't about who you're stuck with. Maybe it's more about who you choose to be stuck with.