Several comments which, at least in part, echo much of what has already been said.
The difficulty many of us probably have: we don't know what you were told when you signed up, we don't know what you paid. It could be that the instructor stated up front what would take place, but it didn't ring any bells with you (not surprising for novice divers). I can not, from afar, suggest nefarious motives, or disreputable business practices - I don't have information that allows me to evaluate that. But, as you describe it, the training appears to be less than optimum. Putting the training issues aside, however, you have established a business relationship, and you have every right, in fact an obligation, to hold the shop / instructor accountable for honoring the contract. Also, based on your subjective perceptions, you should ask him for his agency certification number, and then call that agency to try and determine if he is authorized to teach. Don't simply rely on his name, get his number.
Irrespective of the agency with which the instructor is affiliated, a 2 hour pool session to cover all of the Confined Water skills required for the OW certification is simply absurdly short. The 3 hours of academics is short but not unheard of. In contrast, the pool is where you learn, practice and develop the actual skills required to dive with reasonable safety in open water. For an instructor to say that 'most of his divers get the pool work done in one session' (and presuming he means a 2 hours session) suggests to me a training process that is fundamentally inadequate.
I don't understand why you and your wife were in different gear the second time. Was the instructor trying to give you experience with different types of BCDs (e.g. jackets, vs back-inflate units)?
And that may turn out to be the best solution. But, I would definitely speak - firmly and directly - with the instructor regarding your concerns before doing that.
VERY unlikely. The 4 OW dives are required. Compressing the CW training into one, 2-hour session is nonsensical.
I think it is a good idea. DSS is a great operation, Tobin is very helpful, and going with a BP/W from the start is a very good plan. Don't worry about a 'fight' with the instructor. If he insists on selling you the gear, then your 'cut and run' decision is made for you.
That is the tough call. As most have suggested, your experience to date describes an instructional approach that very few competent instructors would feel good about. But, you have paid for the course - I encourage you to hold his feet to the fire and get what you paid for. And, speaking of that, if you paid for two sets of academic materials, you should a) get two sets of materials, or b) get a partial refund for one of them.
Like a few others, I am not sure I would recommend Cozumel as the first dive destination for newly certified divers. But, plenty of 'newbies' go there, and your decision is already made, so trying to dissuade you is probably ill-advised.
TMHeimer:
Technically, you did not answer the question. The issue is not whether this person has the ability. The question is whether he is appropriately credentialed. Is he an Instructor (not just a DM), is he current / renewed / active with whatever agency he is affiliated with, and is he insured? By the way, if he is NOT current with whatever agency he affiliates with, and he sold you scuba instruction, you can probably demand a full refund, even though you have done academics and a couple of pool sessions. You may not get anything, beyond the satisfaction of sticking it to him. But, if he sold you a program that would presumably end in certification, and he is not credentialed to provide the certification, he misrepresented himself and his product.Pizz:
The difficulty many of us probably have: we don't know what you were told when you signed up, we don't know what you paid. It could be that the instructor stated up front what would take place, but it didn't ring any bells with you (not surprising for novice divers). I can not, from afar, suggest nefarious motives, or disreputable business practices - I don't have information that allows me to evaluate that. But, as you describe it, the training appears to be less than optimum. Putting the training issues aside, however, you have established a business relationship, and you have every right, in fact an obligation, to hold the shop / instructor accountable for honoring the contract. Also, based on your subjective perceptions, you should ask him for his agency certification number, and then call that agency to try and determine if he is authorized to teach. Don't simply rely on his name, get his number.
. 
