When I had a pop-up trailer with canvas sides years many ago, I had a floor model similar to this: (not quite as fancy though...)
https://www.amazon.com/dp/B00B2BTAV6/ref=sspa_dk_detail_5?psc=1&pd_rd_i=B00B2BTAV6&pd_rd_wg=5TOtY&pd_rd_r=RQ41C6PH2MQ8ES9K3WZA&pd_rd_w=lx7Io
The challenge was venting the hot exhaust air produced by the unit. I had to make a 4" hole in the camper floor and adapt a dryer vent hose to the A/C unit to get rid of the hot air. Worked well, but noisy. In your case, you would like have to adapt a vent line to your bedroom ceiling vent.
With that said, as others have suggested, I'd elect to go with an additional roof-top A/C unit if at all possible.