What if....again, just speculating....
What if that night Gerry took the body and left it so it would be found, so they would not be accused, they would get lots of sympathy from everyone, AND Maddie would get a proper burial.
BUT....no one found her. They couldn't exactly lead authorities to her, so they waited as long as they could but then something needed to be done. They couldn't just leave her there indefinitely--so somehow they had to move her so that she could get a proper resting place. Again, I say somehow because I don't know how, but I would imagine using the car would not be out of the realm of possibilities. Maybe after Gerry rented the car for his family and friends to use while they were meeting with the Pope, maybe he went to pick up someone at the airport and disposed of Maddie along the way. No one would suspect them of doing this right before they were to leave for Italy, right? Were there still even searches going on? Were they being watched every second. Did they bury her at Fatima, to have Mary watch over her?
My point is, maybe their initial plan did not work and they had to think of a Plan B.
Maybe. Just speculating. Not accusing.