We might approach Maya Angelou's poem "Woman Work" from a Jungian psychoanalytic point of view or from a Freudian psychoanalytic critical perspective.
Using the Jungian inflection of psychoanalytical criticism, we will focus on the elements of the poem that can be connected to the structures of the unconscious mind (mythic elements in the poem or ideas relating to Anima/Animus or the Shadow). For Jung, the self "embraces not only the conscious but also the unconscious psyche" and we might point to the latter sections of Angelou's poem to identify some universal symbols often associated with mythology -- a realm that Jung connects to the unconscious world of symbols.
In the four stanzas that constitute the second/last section of the poem, the language turns from domestic images to images of nature.
Sun, rain, curving sky
Mountain, oceans, leaf and stone
Star shine, moon glow
You're all that I can call my own.
The speaker of the poem attempts to express her yearning as a desire, not only to be free from her toil, but to be absorbed into the cycle of nature. This longing for the whole or for the transcendent self is closely related to Jung's theory of the maturity of self. When a person's psyche achieves maturity (i.e., individuation), the self comes to embrace all of its parts (the socially derived, the personally derived and the spiritually derived parts).
Thus the poem can be read as an expression of the self reaching toward growth and expansion, or perhaps, more ironically, as an expression of a self turning away from maturity by attempting to escape a total vision of the self that would include toil and social obligation in favor of a Romantic or even paganistic naturalism.
Reading the poem in this Jungian psychoanalytic context as an interplay between ideas of totality and/or wholeness (related to the maturity of the psyche) and division or a divided persona (schisms) might lead to some interesting insights as to the intentions of the poem.
To apply a Freudian interpretation of the poem we might look at how the initial stanza of the poem recounts the many obligations that the speaker feels compelled to fulfill and identify these ideas with the Super-Ego (the part of the psyche devoted to imposing socially derived rules of behavior and articulating expectations, etc.). The latter stanzas then can be related to the Id (the element of the psyche devoted to expressions of deep impulses that spring from the sub-conscious and unconscious areas of the mind).
Seen in the context of the Id, Ego, Super-Ego complex proposed in Freudian psychoanalysis, Angelou's poem can be read as a sort of dialog between two aspects of the speaker's psyche -- that which keenly feels the imposition of social obligation and the force of society and that which feels the impulses of the a-social elements of the self.
We might take note also of the details of the poem that associate purity and freshness with nature and that connect dirt and uncleanness with domestic work. In these details we might find an opportunity to apply some of Freud's views on how the unconscious is expressed through these kinds of associative connections and a person's values, fears and psychological needs are exposed by the implied values expressed. (For example: Is the speaker somehow insecure about her ability to succeed at her domestic tasks?)
This line of interpretation may lead to some insights as to the social commentary inherent in the poem and may lead to an interpretation that stresses the complexity of female identity vis a vis the burden of dealing with filth in order to keep a house clean (for others).