Discuss the relationships between parents and children in Romeo and Juliet. How do Romeo and Juliet interact with their parents? Are they rebellious in the modern sense? How do their parents feel about them?

In Romeo and Juliet, the relationships between the lovers and their parents are multi-faceted. This isn't simply a case of children rebelling for the sake of it, but of teenagers feeling their parents' rules make no sense to them and deciding to follow their own wishes instead.
Romeo's parents are given relatively little stage-time; however, from the audience's limited exposure to them, it cannot be denied they love their son. In act 1, scene 1, Lady Montague is relieved when she learns Romeo was not involved in the brawl which opens the play. Lord Montague is concerned with Romeo's melancholy behavior. He says, though he tries to learn the cause of his son's sorrow, he claims, "I neither know it nor can learn of him," which shows he is involved in his child's life (1.1.137). In the last scene of the play, Lord Montague reveals Romeo's mother died from grief over her son's banishment, once again showing the Montagues' immense love for their son. Romeo's relationship with his parents is not explored. Even though he is a teenager, as a male, he is allowed a level of independence Juliet is not, which is why Shakespeare spends more time on Juliet's relationship with the Capulets.
Unlike Romeo, Shakespeare includes scenes of Juliet interacting with her mother and father. In act 1, scene 2, Lord Capulet reveals he has his daughter's happiness in mind during his talk with Paris. Though Paris is a good match and is eager to marry Juliet, Lord Capulet is concerned that Juliet is too young for marriage and motherhood. Though he approves of Paris as a potential son-in-law, he wants Juliet to consent to the marriage as well. He refers to Juliet as "the hopeful lady of my earth," implying that as an only child, she is all the more precious to him.
Lady Capulet's bond with Juliet is more remote. It's clear from her insisting the Nurse stay with them during their talk of marriage that the Nurse has been more of a mother to Juliet. Juliet is comfortable with the Nurse, while she is formal and polite with her mother. Despite her coldness, Lady Capulet does love Juliet, judging by her distraught reactions to both Juliet's fake death and her authentic one.
For her part, Juliet is eager to please her parents and prizes their approval. When her mother demands to know if she can learn to love Paris, Juliet responds, "I'll look to like, if looking liking move;/ But no more deep will I endart mine eye / Than your consent gives strength to make it fly" (1.3.99–101). Here, Juliet is saying she'll keep an open mind about Paris, but even if she wants to marry him, she will only do so because her family approves.
After marrying Romeo, a union which she knows goes against her parents' wishes, Juliet starts to become more of her own person, moving away from the Capulet prejudice against Montagues. However, it pains her to do so. She is not rebelling for the sake of it or because she has a troubled relationship with her parents. She genuinely loves Romeo and wants to be with him; however, she also wants the stability of familial support. When her parents decide they want her to marry Paris right away and Juliet refuses, Lord and Lady Capulet threaten to disown her should she not obey them. Their bond goes from nurturing to tyrannical, if still well-meaning. As a result, Juliet is forced to pick between the support of her family or following her own desires.
In the end, Romeo and Juliet love their parents, but rebel against both their family's wishes and social norms to follow their hearts. In particular, Juliet's rebellion is socially subversive, since she is a young girl in a patriarchal society defying her father's wishes. She tries pleading with her parents, but they do not listen, so Juliet severs her ties with them in order to join Romeo in Mantua. In this way, Romeo and Juliet could be seen as "rebellious teens"; although, usually in a modern context this refers to teenagers engaging in dress and behavior meant to scandalize their parents. In the case of Shakespeare's lovers, they would rather have their parents' approval and the blessings of society, but that cannot happen.