Parents who are separating or divorcing
An only child becoming a brother or sister
An adoption that brings older or younger siblings into the family
Moving
A single parent dating or remarrying (and possibly bringing in new brothers and sisters)
A parent's boyfriend or girlfriend moving into the home
A caregiver's death or debilitating illness that changes the roles, responsibilities, and expectations for remaining family members
A downturn in the family's financial situation (a parent being fired or demoted, a caregiver getting sick and being unable to work, etc.)
A change in the parents' values, such as them becoming religious when they weren't before, or vice versa
Being sent away to school and experiencing changing family dynamics due to the time away
A parent being deployed overseas for an extended period of time

There are five basic human needs that, when missing from a character's life, could motivate them to pursue this goal. The following needs are all possibilities, but only one of them should be the primary driver for any given character. For more information on the relationship between human needs and outer motivations, please see this Character Motivation tutorial.

Love and Belonging: The most common reason a child would pursue this goal is because they want to preserve the sense of love and belonging within the family. While the circumstances may be difficult, children who want to be loved and accepted will strive to make a changing family dynamic work.
Safety and Security: If a child feels that failing to assimilate into the new family dynamic will result in a loss of safety or security, he may be driven to pursue this goal.