We do learn more about the grandmother's qualities when the family stops at The Tower for barbecued sandwiches. We discover she likes to dance when the mother puts money into the jukebox and plays a tune. When Bailey won't dance with her, the grandmother sways in her chair to the music.
Another quality that emerges for the first time is that the grandmother is willing to reach out and be friendly to people beyond her family. She engages Red Sam in friendly conversation and calls him a good man when he tells the story of letting some "fellers" charge some gas. We learn that she still has the Misfit on her mind, as she brings him up in conversation. We also discover that she blames Europe for taking too much American money.
The grandmother shows that, outside of her family, she can be pleasant and affirming company. Red Sam is not irritated with her the way her family is.