Mrs. Thurlow is a working-class woman who works from dawn to dusk cleaning other people's houses and hoarding as much money as she can. She does so with the expectation that it will help her two sons to get ahead in life. She hopes for them to become shop clerks or butlers or even work in an office. These are humble aims, but they are more than she or her husband have been able to achieve. Her desire that they have a better life motivates and gives purpose to her endless toil.
We don't see anything but the quickest glimpses of her relationship with the two boys, largely because she is gone all the time cleaning. All her thoughts are focused on her hopes for the boys. She uses her little bit of time off to read old newspapers, not interact with her sons. In the one interaction we see before she takes them to their uncle's house, they are building a rabbit hutch and are glad to find out they are staying with their uncle, as he is a carpenter and has tools to help them with the hutch.
The boys later decide they want to remain with the uncle, in a more prosperous home where they will have a better chance in life and possibly can become carpenters. This is good for the boys, and shows that they can achieve their mother's expectation that they have better lives. However, since her husband has stolen and spent the money she saved and been convicted of murder, and her sons are now no longer hers: she has lost her purpose in life and is like a deflated tire.