If the same setup works elsewhere but not in the aircraft, hard to say what it could be. Something has to be different...
Maybe the laptop is running off the battery when in the aircraft? Many laptop USB ports can deliver the usual 0.5A when on mains power but cannot deliver more than say 0.1A when running on batteries. Also many laptops can deliver the full current on some USB ports but not others.
There is no problem with using a webcam+laptop in an aircraft provided it is set up so it is started on the ground and then one does the flight without messing with it. I have done various videos like that, recording direct to a computer (a winXP tablet) using the windoze Moviemaker to record the video via USB. A £50 webcam is pretty good. But I don't do that anymore because a normal camcorder beats everything else on quality. One just needs to mount everything properly so it can run unattended.