Mrs. Kawashima never explicitly states her values, so we must draw conclusions from her actions and her instructions to her children. We can easily see how much she values family; she walks many miles and suffers a lot for them. She values honesty (think of how upset she was with Ko for lying/stealing to get food), education (think of how she signs the girls up for school even though they are poor), propriety (being respectful—think of how she guides Ko on how to act even when hungry and wounded), and compassion (think of them sharing their food on the train).
You can see all of these values in the action of the daughters. They seek their brother for quite some time, and, though they squabble, they give each other gifts. Yoko is honest about her treatment in school in her essay, even though it doesn't make her popular. She is kind to the man with the stutter. They don't meet the Mr. Matsumura in their home, because it is considered inappropriate. In these things, and in others, they show they share their mother's values.