Right here are the facts:
Plane arrived late from PMI, approx. 2hrs. Onblock 12:28 with a CTOT 12:35. At 12:49 they're informed about a new CTOT 12:52. All pax on board 12:50, but due to APU inop and use of airstart they missed their slot. New CTOT 13:39. Around 13:20 PAX started complaining, after swapped their plane for the NYO plane and same crew + Pax continued.
No suh thing then 3 hour delay with pax in the aircraft. The only thing the pax should have done is wait about 9 min more and they would have been on their way airconditioned and all. Instead they chose to stage a mutiny and get themselves another 2 hours delay.
So there lies part of the problem - Ops not having the foresight/manpower to ask for a realistic slot time with the knowledge that the aircraft was going to arrive on chocks circa 1230. This could have been fairly accurately predicted after the aircraft had left Palma so that when it arrived there was a high probability of obtaining a slot time which was achievable with pax on the a/c with no aircon and doors closed for a minimum of time. (With airstart etc how can you stand a fighting chance of making CTOT 1252 when ready at 1250, also bearing in mind the discretion on slot times is really for ATC?).
Even 30 minutes with doors closed in these OATs is obviously excessive - as soon as the revised CTOT of 1339 was known why not open the doors or request ATC early start and push to take delay at holding point with engines running?
Am not saying the customer is always right but if I had been seated on that aircraft with young children, especially after a 2 hour delay, I would probably of been of the same sort of mindset as these passengers.
Finally, we don't know how much information was communicated to the passengers and whether it was communicated effectively.