Adrienne Rich’s "Living in Sin" portrays the relationship between a man and a woman and the woman's expectations and dissatisfaction. In order to come up with some great thesis, you should choose a particular aspect of the poem which you wish to explain and support.
My suggestion is to focus on the contrast between the woman's expectations and the reality of her situation. Therefore, I would say that the poem demonstrates the tension between the woman's romantic and unrealistic notions of love and the cold, frustrating reality which dispels such idealistic notions. In order to support your thesis, you should refer to the poem to find the contextual clues.
The studio that is described at the beginning of the poem is symbolic of the relationship the woman is in:
She had thought the studio would keep itself;
no dust upon the furniture of love.
The furniture is not just the furniture in the studio, but "the furniture of love," which means it is a metaphor for their relationship. The woman thought that, just like her studio, her relationship with the man would be alright, with "no dust" upon it.
The beginning of the poem provides some evidence referring to the woman's idealistic notions of what the studio would look like and what her relationship would be like. Her unrealistic image of the studio, consisting of "a plate of pears, a piano with a Persian shawl, a cat stalking the picturesque amusing mouse" is in stark contrast with the reality of the studio, embodied by the noisy taps and grimy panes.
The poem continues to give us more examples of the unattractive appearance of the studio, which she thought would be the perfect love nest. "The scraps of last night's cheese and three sepulchral bottles" and "a pair of beetle-eyes" all underline the filthiness of her surroundings.
Then, the poem moves to the description of the woman's man, who is depicted as uninterested and self-absorbed. He is unwilling to do anything to make their relationship better:
Meanwhile, he, with a yawn,
sounded a dozen notes upon the keyboard,
declared it out of tune, shrugged at the mirror,
rubbed at his beard, went out for cigarettes.
The future of their relationship is very uncertain because although she can still succumb to her idealistic reverie during the night, the day shines light upon the grimness of reality:
By evening she was back in love again,
though not so wholly but throughout the night
she woke sometimes to feel the daylight coming
like a relentless milkman up the stairs.