Thanks for sharing your experiment. What you found does make sense... with good air flow, the inside temp should be nearly the same as the outside air temp.
The sides and roof of most trailers are white. In theory, that should reflect most of the sunlight and result in little temperature gain through those surfaces. With sun shining through the windows, items on the inside of the trailer would get hotter than the air temp. With the windows closed, that additional heat would stay trapped inside the trailer.
If you can, try your experiment with material covering the OUTSIDE of the windows. It may be more effective to stop the sun from heating the inside if you stop it before it shines through the windows. And, like you said, it seems that adding film to the inside
of tinted windows may not help much.
To cover skylights, these and similar items are available but making your own should not be difficult... Robot Check
I plan to conduct some experiments regarding heat gain through windows etc., but that is unlikely to happen this season.