The relationship between The Tempest and Mama Day is very vague. You could say Mama Day is a loose interpretation of The Tempest, however these works are so different that if you had no idea to connect the two; you wouldn't. But since we read The Tempest and Mama Day consecutively, it is easy to parallel the two, and we probably should since this class's focus is American Shakespeare after all!
The obvious correlations would be the tempests (violent storms) in each and the fact each of them are set on an island. Other parallels you could make would be with the characters. The first being with Mama Day and Prospero and second, Ruby and Sycorax. Mama Day's "magic" per se is highlighted in the book as beloved, good, and helpful which can be associated with Prospero's magic in The Tempest because Prospero was never seen as vengeful or harmful to other with his magic, just like Mama Day. Ruby on the other hand dealt with black magic. By poisoning Cocoa with nightshade she showed her immoral behavior and wickedness- as shown in the witch like figure of Sycorax when she is cruel to Ariel in The Tempest.
Another correlation could be with Caliban and George. In The Tempest, Caliban was the outsider on the island and he was taught by Prospero and Miranda the way of the land and how to speak their language. They also put him to work by having him do chores for them and get them essentials they needed for survival.
Some of this same stuff happened to George as well when he went to Willow Springs and stayed with Abigail and Mama Day. George was taught some things by them but was ultimately put to work by them. They had him fixing their homes and helping them with farming, as well as trying to get him recognize what they believed in and how they lived in a place like Willow Springs.
There are many aspects in Mama Day that are different than The Tempest, to name a few basic ones there's the fact that the tempest occurs at the end of Mama Day and at the beginning of The Tempest, there are fatalities in Mama Day and not The Tempest, and finally that George and Cocoa don't get married on the island like Miranda and Ferdinand in The Tempest. I think Naylor was inspired by Shakespeare since he was an amazing playwright. However, I don't think she reworked the story, I think she used Shakespearean elements, just like a lot of other writers, to tell her own unique story better. A lot of the time people unconsciously put other works into their own and not even recognize it. I think this was the case with Naylor because her story, especially the plot has no validity with Shakespeare's plot in The Tempest.