Why is it that white fish do not have as strong of a "fishy" taste as other fish?
Kudos to your wife for giving it another shot!

Let me start with what I feel is the most important part of my answer: find a good fish monger and make friends. If the supermarket is the best you can find, so be it, but learn the name of the person behind the counter, ask about the fish, be interested. Ask what's just in, ask what's fresh. If the fish is frozen at sea, ask if you can get some from the freezer instead of the stock in the case that's been thawed and sitting all day.

Ask to touch and smell the fish. Look at the stock - do the whole fish have clear eyes? Does it smell like a dumpster? Getting the freshest, best fish will help you and your wife enjoy it more. Some good suggestions here on shopping for fish.

Now, on to your bullet points. Fish should never smell or taste "fishy". Fishy smelling fish is a sign of bad fish.

I find that a lot of my friends who say they don't like fish have had experiences with poorly handled or old fish. Fish must be fresh (or frozen at sea and handled properly afterward) to be good.  I've stopped ordering fish in restaurants unless it specializes in fish (and I don't mean Red Lobster) or is well known for their freshness.

That said, some fish is certainly more strongly flavored than others. I found this nice chart here with a few varieties of mildly flavored fish. I do agree that flaky, white-fleshed fish is generally the mildest. Flatfish, like sole or flounder tend to be consistently mild. Tilapia has become an extremely popular fish lately.

However if you do find a good fish monger, talk to him about it and you should be able to find plenty of interesting venues: monkfish has been called the poor man's lobster, and I had some arctic char the other night that knocked my socks off.

As for why white fish tends to be less strongly flavored than meatier fishes, I can't really answer authoritatively. My guess would be that meatier fishes tend to be more oily and fatty, which equals more/stronger flavor.