Shakespeare certainly portrays family relationships in Romeo and Juliet as being strained and distant. It's very evident that both the Capulet and Montague parents care very much for their children, but it's also very evident that, typical of the times, the parents are very emotionally distant from their children.
We see evidence of just how much Romeo's parents care for him in the very first scene. Lord Montague expresses a great deal of concern for Romeo because he has been seen morning after morning at dawn, on a certain part of town, "[w]ith tears augmenting the fresh morning dew," meaning that he has been seen crying (I.i.128). Romeo is also staying out all night long and not going to bed until morning. Because of this behavior, Montague begs Benvolio to try and find out from Romeo what is making him so sad. We especially see Montague's concern in the lines, "Black and portentous mist this humour prove / Unless good counsel may the cause remove" (137-38). In other words, these lines are saying that Montague believes Romeo's emotional state may cause him harm unless someone helps him by giving him sound advice. However, Montague also shows in this scene just how strained and distant his relationship is with his son. He shows this when he also states that Romeo refuses to talk to anyone, including his father, about his problems.
Juliet also proves to have a very distant relationship with her parents. It's very obvious that her father loves her very much and wants what will make her happy, as we see when he refuses at first to give Paris permission to marry her. It's also very obvious that Juliet aims to be respectful to her parents, as we see in Act 1, Scene 3 in which she converses with her mother. However, Juliet also feels compelled to deceive them, and later when she refuses to marry Paris, her father threatens to disown her, showing that she has a very strained and distant relationship with her parents.