The UAE isn't that strict at all, and Qatar is similar in that you can have a small libation in the hotel bars. The golden rule is, if p1ssed, get a recognised taxi home and go straight home; don't go swanning about the place as if you were stil in the UK.
Sqad, would love to swap drunken Saudi tales; I have many happy memories of the pace.
When in the UAE I had occasion to go and "rescue" hungover staff from the local police station. The Chief Constable was a wily old b*gger and was well used to drunken Westerners. A night in the slammer with about twenty locals and a hole in the ground for a toilet, (literally), usually convinced them to behave in future. When releasing them Fahad used to let them get near to the gate and then call them back to clear up some "paperwork". He and I would then enjoy a small nip while this non-existent paperwork was cleared up.
If your son were to transgress then deportation is the likely outcome.