Grandma Dowdel is a force to be reckoned with—in fact, she's something of a legend in her small town. When she takes Mary Alice in for the year, she exposes her granddaughter to the full range of her eccentricity, and the kinds of scrapes and situations that she gets into.
First of all, the book makes it clear that Grandma Dowdel is not the kind of grandmother who prunes roses and bakes cakes all day (although she is the best baker in town). No, Grandma Dowdel is a tough cookie, and her reputation is known far and wide. This is communicated right away when Grandma Dowdel picks up Mary Alice at the train station:
Grandma stopped dead and spoke clear. "You're going to school. I don't want the law on me."
"Grandma, the law's afraid of you. You'd grab up that shotgun from behind the woodbox if the sheriff came on your place." (1.19-20)
And in addition to being a rather intimidating figure, Grandma Dowdel doesn't seem to have a lot of sympathy for Mary Alice. Not only does she tell the school principal, "Boys is bad business…Though girls is worse" (1.44), she also caps the end of Mary Alice's challenging first day by telling her, "And you better settle in too, girl. Or I'll butter your paws" (1.140).
At this point, it seems pretty safe to say that Grandma Dowdel is a believer in tough love. We see the "tough" right off in her gruff greeting to Mary Alice at the train platform:
You couldn't call her a welcoming woman, and there wasn't a hug in her. She didn't put out her arms, so I had nothing to run into. (1.6)
But the "love" reveals itself a little more slowly.
Despite her toughness, Grandma Dowdel uses her powers for good. She may not be well off, but she's keenly tuned into the economic strife around her, and does everything that she can to help those in need. For example, she makes it a point to take more money from those who can afford it when selling burgoo at the annual shoot-out, and gives food for free to those who are struggling:
In short, she got more than a dime off everybody, except from those she knew couldn't pay more. In some cases she could make change, in others she couldn't. Once, I saw her palm the dime back into the hand that offered it. (3.61)
Grandma Dowdel isn't taking money or food for herself; she's always doing it for other people. And that generosity extends to her own family. She spends all winter trapping foxes and selling their furs, and it's only later that Mary Alice realizes she was saving up to buy Mary Alice and Joey tickets to see their parents in Chicago for Christmas:
After we got home that night, Grandma showed me another ticket. It was a round-trip to Chicago for me, so I could go with Joey to have some Christmas with Mother and Dad. It must have cost Grandma her last skin. (4.119)
She doesn't even buy herself a ticket, even though it means that she'll spend Christmas all alone. She does it all for the kids, because she knows how much they miss home.
All of these little things that Grandma Dowdel does show us that she is, indeed, quite loving beneath her gruff exterior, and we have to rely on her actions instead of her words to show us the truth of her character.
After the tornado, for instance, Grandma Dowdel is quite concerned for her friend Effie Wilcox:
Grandma nearly fell back. "Her privy's gone. What if she blew away in it?" (7.54)
But when Mary Alice tries to get her to admit just how important Effie is to her, Grandma shoots her down.
We left then, Grandma bustling to prove she hadn't given two hoots about Mrs. Wilcox.
[…]"Grandma, is Mrs. Wilcox your best friend?"
"We neighbors," she said. (7.64, 7.69-70)
Still, in the end, we know that Grandma really does care about her friends and neighbors and she certainly loves her granddaughter. Indeed, her eyes are "pink and glistening" at the idea of Mary Alice going back to Chicago (7.106).
But it's not that Grandma Dowdel changes significantly over the course of the novel—it's more that her character is slowly revealed to us—and to Mary Alice—despite her attempts to keep her tenderness under wraps.