16' trailer with pop out tent sleepers is just a very large tent... ;)
Is this a pop up trailer or a hard sided trailer with beds on each side?
I've seen pop ups with an A/C unit on the hard pop up roof part.. But, I don't think you will be able to sleep with the fan noise these kinds of units produce..
Heck, even in my 22' TT with a roof top A/c unit, it's only good to keep it cool if you don't mind all the noise..
If it's that hot, we just open the vents and the windows and sleep on top of the bed at night, because there is no way to sleep with the A/C running all night long.. Just no way.. Think "Jet Airliner"... :)
Anyway, hope you find your solution.. Been there, done that in tents for decades and survived... ha, ha....
Good luck!
Mitch