Question: Why would Kyle assume that her daughter was hidden inside the casket? Only she knew the code.
Answer: Because after searching the entire plane for her daughter without finding her, it was the last place left she hadn't looked in. It was a desperate, last-ditch attempt to try anything to find her. By now, Kyle may have been suspecting that her daughter's disappearance was something more than a missing child on a plane.
Actually the last place she hadn't looked before the casket was the avionics room in the nose of the plane, which is where Julia was hidden. And to be honest, I have no idea why Kyle didn't assume her daughter was hidden there, and search there before the casket instead of near the end of the film especially knowing it didn't have a lock, unlike the casket.
No kidding. I mean how in the world did she miss that? She's an avionics engineer. She designed the darn plane.
Question: I realised a couple problems with Carson's plan. I understand that he murdered her husband by pushing him off the roof so he could hide the explosives in the casket, and that once Kyle and Julia boarded the plane and fell asleep, he could kidnap Julia, and Kyle would have a reason to open the casket. The first thing I don't understand is how did he get Kyle's husband to come onto the roof? What if a different person came onto the roof instead? Or what if multiple people came onto the roof? The second thing I don't understand is how did he know Kyle would decide to leave Germany and bury her husband's body in New York? What if she decided to store her husband's body somewhere and deal with it later? Or what if she decided to bury it in Germany instead?
Answer: Carson was a member of a conspiracy, not the sole person who planned and executed the entire plot. His cohorts, which included the funeral director, carried out the first phases by murdering Kyle's husband, then the mortician assisted Kyle in making the arrangement to transport the casket back to the USA. It is not important to the plot to show exactly how and by whom Kyle's husband was thrown off the roof. We only need to know that he was murdered as part of the plan. Kyle's specific travel arrangements would be relayed to Carson who could then get himself assigned as the air marshal on her flight so he could carry out the final stage of the plan.
I don't know that Kyle would have taken time to arrange for her husband to be transported back to USA especially since she would have been extremely busy helping design/build aircrafts. She's an avionics engineer after all.
Most people would take time off work to bury their loved ones or transport them for burial.
Answer: I don't think Kyle was looking for Julia in the casket. The crew and air marshal were convincing her that she was delusional. They had also told Kyle that Julia died with her husband. I believe she was looking in the casket to see if it was Julia's casket instead.