How does the information about Ruth impact the reader's understanding of the relationship between the Putnams and the Topsfield-Nurse faction?

Ruth is the only one of the Putnams's children to survive. Ironically, given the fact that her parents are such enthusiastic witch-hunters, she herself has been involved in the strange, witchy cavortings in the forest along with Abigail Williams and the other girls. The Putnams, like Reverend Parris, are keen to protect their family's reputation from the imputation of sin. To that end, they put the focus on other people in order to detract attention from what Ruth has been up to.
Also, Mrs. Putnam has become seriously unhinged by the loss of all seven of her previous children, so when she sees Ruth lying still in bed with a glazed expression in her eyes, she fears that her sole surviving child has been bewitched. Ruth never speaks a word in the play, but she doesn't have to. Her strange demeanor is enough to convince her parents—and soon the whole town—that there are dark forces at work in Salem.
Mrs. Putnam takes this opportunity to ramp-up the land war between her family and the Topsfield-Nurse faction, using the phony witchcraft scare as a weapon against their political rivals. Rebecca Nurse is a woman of unimpeachable virtue. Yet the Putnams have no hesitation in branding her a witch simply because she belongs to a rival faction. Rebecca's faction blocked the appointment of Bayley, Thomas Putnam's choice for the ministry, so the Putnams have been itching for some payback ever since. Ruth's unusual behavior, lying still on her bed without saying a word, provides a catalyst for what is to follow. The Putnams exploit their own child—whom they believe to be bewitched—to even the score in their ongoing political squabble with the Topsfield-Nurse faction.