The family dynamics of Romeo and Juliet can seem pretty strange to us in the modern day. At this time in Europe, lifespans were much shorter, so people were considered full adults around the time they became teenagers. This meant that they were expected to take on new responsibilities, including marriage and raising a family. Romeo and Juliet's families do want their children to do well in life, but they are more concerned about these two young people fulfilling social expectations than their true happiness.
One thing which may seem especially unusual to us but was quite common in Shakespeare's time is the character of Nurse. Throughout history, wealthy families of Europe would often employ a nurse (also called wet-nurse or nanny) to care for their children. These women would care for the children as if they were their own, breastfeeding infants and serving as confidante in the older years. As we can tell in Act I, Nurse has a lot of affection for Juliet and fulfills the roles her mother does not. Lady Capulet is really more of an administrator for Juliet's appearance in society, hence her desire for Juliet to marry!
On the other side, Romeo is offered a little more independence than Juliet because he is a boy. He is free to spend time with his male cousins and even wander among the trees by himself while he daydreams. Romeo's parents find his introversion a little odd, but nonetheless want him to do well.
The family roles of the Tudor and Renaissance period did not really allow for the kind of emotional connection most parents and children share today. Only in the most serious of cases would a noble parent step in to discipline their child, and they spent even less time "getting to know" their children. To us, this may seem cold or cruel, but it was the reality of life for wealthy Tudor and Renaissance people.