What was the relationship like between Tituba, Betty, Abigail, and Rev. Parris from "The Crucible"?
Literally speaking, Reverend Parris is Abigail's niece and Betty's father, and Tituba is his servant in the household.
We don't know much about the relationship between Betty and Rev. Parris; we do know that he is worried about her, and he is a single father. Betty misses her mother, because at one point she cries out, "I want my mama!...I'll fly to Mama!" and collapses on the bed, crying for her mom. So, even though Rev. Parris seems concerned about her health, Betty seems to want her mother, and afraid enough of her dad that she goes inert at the possibility of being punished by him for dancing in the woods. Abby shows mixed attentions to Betty; she is kind, gentle and imploring ("Betty, dear, wake up now") to threatening and incensed (she "smashes [Betty] across the face: 'Shut it!'"). So, Betty is obviously intimidated and frightened of Abigail.
Rev. Parris took Abby into his home after she was fired from the Proctor place, and their relationship seems a bit strained. She is trying to be respectful to him, but resents being there, and he is trying to be helpful and kind, but is resentful of the rumors floating around about her reputation. He states to her,
"I have given you a home, child, I have put clothes upon your back-now give me upright answer. Your name in the town-it is entirely white, is it not?"
His hesitation and doubt show here, and Abby gets defensive, and states, "with an edge of resentment:...There be no blush about my name." She resents that he would even bring it up, and he resents that he might be harboring an immoral girl in his home.
The only clue we get about the status of Tituba and Rev. Parris comes when she is pretending to confess to witchcraft and states rather ominously of the Devil, "how many times he be me kill you, Mr. Parris!" Here, we might get an undercurrent of hatred for Parris on the side of Tituba's part. Tituba seems rather motherly towards Betty; she states of her, "My Betty be hearty soon?" She calls Betty hers, and is worried about her health. So, there is a fond affection between the two there. Then, Tituba and Abby seem to be close enough that Abby trusted her to ask for a death potion. In fact, Tituba states that Abby "beg me to conjure" and to chant spells. So, they were friends, or co-conspirators. That is, until Abby turns on Tituba, blaming her for her evil doings in the forest. At that point, Abby shows how she is willing to throw anyone-friend or foe-under her feet in order to not get in trouble.
I hope those thoughts help; good luck!