I found this part to be the most interesting. When you talk about the north end, I assume you are talking about Barracuda Reef and San Juan Reef.My nephew was experiencing his first ocean dive. A repair to my regulator was not finished in time for our trip so I used the dive shop's well worn equipment. This was my first and last time doing this. The equipment though used was functional. One unit only had a pressure gauge and the other had both a pressure gauge and a depth gauge. Neither had any timers or dive computers....
This is were the week had the potential to go wrong. The Dive Master took us all spear fishing on the North end of Cozumel. The strong current ...
The first two operators I used on my trips to Cozumel would not go to those reefs at all. They said they were too dangerous because of the currents. Frustrated, I called several others before I found an operator who would take divers to those reefs. I have since dived them several times. Once was surprisingly easy, another was difficult, and the third was one of the most difficult ocean dives I have ever had because of the currents blowing diagonally across the reef, constantly trying to take us off the reef. It doesn't sound like your dives were as bad as that, but they had the potential, and I am surprised they would take a new ocean diver there.
Dives in Cozumel are required by law to be led by a DM, and one of the reasons is because of the currents and the need to make sure that everyone gets picked up by the boat at the end of the dive. Sending people up in pairs without any kind of signalling device is pretty risky in any kind of drift diving--if the boat does not see your ascent, they may miss you entirely and you could be drifting on the surface for quite some time while they look for you. That is why the DM's job in Cozumel, unlike most resort dive locations, is to keep an eye on people. When I have dived there and had people ascend in pairs rather than as a group, the DM sent a DSMB up first, and everyone stayed with that line. That way they could feel confident that everyone would be on the boat at the end of the dive.
A number of years ago two teachers who worked in the same school district as I were diving in Cozumel on a reef that had a tough current. The DM did not see them when they were apparently blown off the reef. I say "apparently" because no one ever saw them again.