Learn English – What does “a time that never was” mean

Issue in this context means a condition which has caused a person (in this case the mother) to manifest an undesirable behaviour or mental state. It is an informal term from psychoanalysis.

"Please work on your issue,lady!" is an admonition to the mother to seek out the root cause of her behaviour, which the speaker clearly feels is inappropriate, and to reconcile herself with whatever this experience was so that she can stop the undesirable behaviour.

In contrast to Irene's answer, I would argue that "issue" used in this context is not that the mother has a problem, but rather that the mother, or more particularly her inappropriate emotional response to some past experience is the problem.

For example, a child who is not this mother's favourite could be said to have a problem, but you wouldn't tell this child to "work on their issue". Issue in this context is internal to the person with the issue. The mother's inappropriate response to some past experience is her "issue" which can in turn cause "problems" for her offspring.

The meaning is most likely from this definition of fast:

a : wild
b : sexually promiscuous

From Wiktionary:

Having an extravagant lifestyle or immoral habits [from 18th c.]

And from Etymonline:

The sense of "living an unrestrained life" (usually of women) is from 1746 (fast living is from 1745).

Without delving too far into literary criticism, the preacher's daughter, Sabbath Lily, is often the victim of men in the novel and is later revealed to be a nymphomaniac. So this sense of the word is undoubtedly what was implied.