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The moving carrier is an instance of FGAIShip, one of the AI object types. These are not currently seen by the hitlist, which is where objects get their solidity. A moving object would have to interact with the hitlist on every frame.
Wind/turbulence effects are possible; the FGAIThermal class which models a thermal. It modifies the value of wind-from-down when the "user" aircraft is within the thermal's radius, creating a "rising column" of air. Causing a ship to bob up and down can be modeled by adding a periodic altitude adjustment to the ship's location. That's the easy part. What will be needed is a method where we can query for the position of a surface element (triangle/whatever) and its speeds (longitudinal/rotational) dependent on a given position (usually the contact patch position). Also for the cat and the wires we will need to query those objects and such details.