Quote 1
"I'll be gone tonight and all day tomorrow, and I don't want the milk left out where it'll sour. I won't pay for it. I'm taking my grandkids on a visit to my cousin Leota Shrewsbury." (2.41)
Grandma Dowdel just made up a family member in order to get back at the Cowgill boys for blowing up her mailbox. She doesn't see anything wrong with pretending to be a kindly old granny who's taking her grandkids for a family visit.
Quote 2
Grandma waved that away. "Don't give it a thought. You can take my grandson instead," she said. "If he wants to go."
The heavens opened. I thought I heard celestial music. Somehow I was up in the front seat of the plane, buckling myself in with trembling hands. (4.118-119)
Grandma Dowdel may not be the most affectionate woman in the world, but she still wants her grandchildren to have what they want. She even lies and says that she won the pie-baking contest so that Joey can get his first ride on an airplane.
Quote 3
Then as if a sudden thought struck her, she nudged me. "And you can give this boy here a two-dollar bill." She nudged Mary Alice. "And fair's fair. Give this girl two dollars too." (6.138)
Maybe it's wrong of Grandma Dowdel to shake down the banker for money, but at least she's doing it for her friends and her grandkids, and not for her own personal gain. She's always got Joey's and Mary Alice's backs.