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If your plan is to get certified while in Hawaii for two weeks, it would seem you will be getting Padi certified. With private lessons, his should take about a week, including the requisite dives/in-water training and classroom time. Including I believe at least one night dive. You will have enough to concentrate on being a new diver. Taking your mask off and having to put it back on at 45 feet is tough if you have never done it before. Having your air turned off at 30 feet by your instructor, is enough to concentrate on as you surface at the correct speed without having any air to breath.
Leave the underwater camera at home for your learning period.
But on to your question about equipment:
#1: considering this trip is really going to be limited in terms of recreational diving, I would get the Panasonic or Olympus point and shoots that are usable underwater and use them mostly for snorkeling and maybe a few shots of "each other" when diving.
#2: to be properly set up for underwater photography at below 30 feet, the lighting is actually more important than the camera! Without the proper lighting, you won't get the color at this depth. But if you insist on proceeding for this trip, I think the company is Sea and Sea that makes a rather inexpensive UW camera and lighting system that you could probably get for about $1,000 (purely an estimate).
#3: Know in advance that almost any picture you take underwater, you will be very close to your subject. In many cases a few inches away and for larger fish and sharks, etc. . . a few feet. Hawaii has decent water clarity but not the best. Most of my UW photography was done in the Rock Islands in Palau, very good clarity, 2-3 times that of Hawaii as measured in distance. I have pictures of sharks from 10-12 feet away - they are blue! and that was with two large flashes. But it was also with a film camera quit a few years ago. I lived in Guam for a decade, so-so water clarity, 100-150 feet on good days. Anything below 45 feet deep had to be within 6 feet to get a really respectable shot.
My advice, start with a waterproof digital P&S. It will be great on this trip, you can take it swimming or surfing, on the beach, in the rain, etc. . . You can take it diving (up to a specified depth). But you need to determine when doing this if you really want to spend your time underwater chasing the shot or enjoying the beauty? You'll be amazed how much you can miss when you are concentrating on the shot . . . hopefully it won't be your dive partner in trouble!
The most important thing when starting is safety and awareness. Master this before concentrating on the extraneous act of UW photography. I think in the long run you will be much better and happier. IMHO
FYI, I am/was aware of the trip had already taken place, my post was general purpose.