I don't think many people (read it again... **many**- that means a lot but not all) who are afraid of certain things once attempted are all that afraid of it anymore. Conquering your fears sounds corny, but it's usually true. There's a little switch wired into our brains that tells us "Don't do this, it's hazardous" and it makes us not want to do it. Once you've actually been able to flip that switch off just long enough to get yourself into the seat of a rollercoaster for example and now the ride is out of your control and you experience it and are now familiar with the experience (and its actual safety) that switch tends to become easier to switch off, if the need to do so even still exists. I'm being a bit of a hypocrite here as I refuse to go skydiving or bungie jumping etc. but I think that's a bit more rational than a fear of a Disney ride which tend to be some of the safest things you can do but still they're both actually less hazardous than driving on the highway.
Now with that being said some people either a) are so afraid they refuse to let themselves enjoy the experience and continue to tell themselves "This is dangerous, be scared" and will not enjoy it or b) have an aversion to the actual sensation which I'm not really sure there's much you can do about. If you seriously think your wife, kid, whoever you try to get on a ride will be affected in such a way it's probably not the best idea to push it; especially not all at once. Start off smaller and work your way up. I've known people who have literally lost trust in others to some extent because they convinced them something "Wasn't that bad" and they didn't agree and it ruined their days. I think it's all a bit extreme but who am I to judge?
Again, I'm possibly not even giving the best advice reflecting myself as I used to be dreadfully terrified of inversions (loops, rolls, corkscrews, etc.) on rides and my parents took me on a single inversion coaster and I FREAKED but then as I got older I realized "These rides are safe and everyone seems to have such a good time- try it" so I went on the biggest baddest inverted coaster I could find at Six Flags rode it and haven't looked back on coasters since. Sometimes I guess you just gotta take the plunge.
As to the OP- I personally think Splash is much "worse" if you will than Big Thunder. While Big Thunder is constantly a quick ride, there are absolutely NO big drops; the biggest drop can't be more than 20 feet. Splash is twice that and probably almost double in steepness. It's a fairly long and fast drop that I honestly think is "worse" than Tower of Terror which to me doesn't quite hit the pit of your stomach the way Splash starts to at the end. The thing about Splash is it's over in literally under 2 seconds. And if there's a way to convince your wife to try, I'd say it's that- appeal to her that you'll get a memory to keep for years to come at the sacrifice of possibly being in either physical or psychological discomfort for a couple of seconds (though I guess psychologically, it'd be from the moment she steps in line but Splash does a great job at taking your mind completely off the drop until that final incline once you're on it). Also, if you're afraid of Big Thunder maybe you should agree to ride it with her if she's willing to ride Splash. They're right next to each other, kind of a hard cop out!
Good luck!