What is the significance of the play Lover's Vows, and what does it reveal about each character in Mansfield Park?

Lover's Vows is a play that is significant because it reveals information about the integrity of the main characters in the novel. First, it is a play that the family knows their father, Sir Thomas, who currently is in Antigua, would not want them to perform because of its racy subject matter. Nevertheless, Henry and Mary Bertram, along with Tom and Maria, push hard for performing it, with the support of Mrs. Norris. Edmund and Fanny resist, insisting the play is inappropriate.
We see through their advocacy of the play that Tom and Maria are willful and determined to do what they want. The play is a way for Maria to engage in a covert flirtation with Henry, even though she is engaged to Mr. Rushworth, who also takes part in the play. Under the guise of the lines of the play, Maria and Henry can engage in love talk that normally would be forbidden. Maria's behavior during the play rehearsals foreshadows her eventual running off with Henry.
Edmund shows a lack of integrity that he will come to regret. Despite his best instincts, the desire to play a love role opposite Mary, with whom he is completely besotted, overtakes his morals, and he agrees to participate in the production. This symbolizes the allure of the harp-playing siren Mary, who can tempt him to abandon his values. If he had married her, more of this might have occurred.
Fanny, however, stands firm, even when Mrs. Norris verbally abuses her for not participating. She shows her integrity in refusing to do what she knows is wrong. She also shows her kindness, patience, and compassion as she helps Mr. Rushworth learn his lines—and also is able to comfort him in small ways in his distress over his fiancee's "allowable" flirting with another man. Although Fanny does not like to act, she learns everyone's parts, showing that she is intelligent and has made a habit of studying others to survive as a poor relation.
Mrs. Norris shows that she will do anything to pander to the whims of her nieces and nephews. The play will mark the beginning of her loss of esteem in Sir Thomas's eyes, for when he returns he won't be able to understand why she didn't stop the play.
Finally, Mary and Henry show their urban worldliness. Doing a play—even an "off color" one like this—doesn't bother them a bit. We also see through this play, as we will see later, how deeply Henry likes to play parts. It is consistent with his deceptive nature that he will play any role that strikes his fancy at the time—his sincerity is never more than skin deep. He is the one, more than anyone, who loved rehearsing the play, and he is the most unhappy that it is shut down. This foreshadows how much his wooing of Fanny will become a game, one he quickly abandons when another temptation comes along in the form of Maria.
As seen, the play offers insights about who the characters in the novels are, especially their weaknesses, and the ways they can be tempted.