This book has several conflicts, but here are the two biggest external and internal conflicts, on which the plot revolves.
The first is the external conflict the family faces at the very beginning of the story, when they must enter the witness protection program. Consider the stress of a sudden move anyway - add to this a change in lifestyle and identity - not to mention the persistent fear of being found, despite measures of safety. This conflict is the foundation for the entire plot.
The first external conflict of course leads to the biggest internal conflict, which is the question of identity for each character. The entire book is a story of the struggle to find or maintain an identity - which the characters realize in the end, could only be done because they are a family.