The children's personalities complement each other in their mission by blending their strengths and skills together. For example, Emily's creativity and out-of-the-box thinking pair well with Alex's logical reasoning and analytical approach. This allows them to tackle challenges from multiple angles and come up with innovative solutions. Additionally, Sarah's leadership skills and ability to motivate others work harmoniously with Jake's attention to detail and focus on planning, creating a well-rounded team dynamic that leads to success in their mission.