I am required to write a comparative essay about parenting. The novels that I want to use are Night Waking by Sarah Moss and Lanark by Alasdair Gray. I'd focus on Anna and her children and Thaw with his father or his parents, but I am confused about the aspects that I should cover. I know that Night Waking has some sort of feminist or Gothic elements. I just cannot decide how to compare it with Lanark. How do I construct the essay? What literature do you recommend to support my analysis?

The first issue you have here is that your essay needs to have a coherent point. Night Waking is a novel about parenting, told from a mother's perspective. Lanark is really not about parenting and is not really the ideal choice of a second work. I suspect some of the reason you may be struggling with this assignment is that the choice of Lanark doesn't appear to have an obvious rationale. That being said, the main approach you should take is one contrasting the two works.
Introduction: Your introduction should set out why you chose these two works and mention that parenting is treated quite differently, being central to one of the books and peripheral to the other, with the male writer less focused on parenting than the female one.
Authors: Here you might compare and contrast the two authors, mentioning that Gray is substantially older than Moss, and is writing in the tradition of Joyce, addressing the question of the formation of the artist, while Moss is of a younger generation, addressing issues of the conflict between parenting and intellectual life for a female scholar.
Point of View: Night Waking talks about parenting from the perspective of a parent. In Lanark, Thaw looks back at his childhood, and while parents are present in the novel, they are only seen through Thaw's perspective. He is parented rather than parenting. 
Gender: You might argue that the gender of the narrators is what makes the female protagonist engaged in the task of parenting and the male someone who is more detached from the act of parenting. Much of feminist literary theory discusses this. One useful starting point might be Stabat Mater by Julia Kristeva, a landmark essay on this theme. Hansen's Mother Without Child is also useful. The MLA International Bibliography might also be a good source of references to relevant scholarly works.
Conclusion: Your conclusion should discuss how either (1) the analysis of parenting helps us understand the novels better or (2) how the novels make us aware of some important issues concerning parenting.