I do understand your frustration, too! Don't give up! Your new camera will get easier to use the more you practice, and in a few months you'll be LOVING it, I'm sure.
But I do want to agree with you -- unless you know what you're doing and how to do it, the initial pics from a "fancy dancy" dSLR can be MUCH WORSE than those from a good quality zSLR. You really have to know what to tell your dSLR to do. BUT...once you know it, your pics will do an amazing jump in quality.
Indoor portraits are hard. Give yourself a bit of a break on this one! For instance, I have a D300 and some good lenses. But even with a fast lens, and even living in the land of bright sun (Arizona!), there is just not much light indoors. You have to know when to use your flash, how to bounce it, when to bump the ISO and how much, when to use a tripod and when to safely hand-hold. If you're still sort of playing around, you might not get the "perfect" settings for your camera. And a good quality zSLR on auto can figure it out by itself and get a better pic, kwim? But honestly, give yourself time and just practice a LOT, and it will get much easier! And you will start getting those pics you crave.
I usually shoot on aperture priority, unless I'm using my studio lights (then I use full manual plus a lightmeter.) I rarely use shutter priority. I actually only use the tripod for studio lights too, b/c I take tons of pics of my dd and the tripod just gets in the way (she's too fast and zippy!)
About "sunny 16" -- forget this for now! Your camera has a good light-meter built in, and you don't need to memorize this stuff -- your lightmeter will always tell you what aperture you need for SS, or what SS you need for a given aperture. I'd say to just focus on understanding how depth of field changes when aperture changes, and how your shutter speed changes as aperture changes.
Just keep looking at your setting in Photoshop for both good AND bad photos, and start figuring out what combos of aperture/SS/ISO/flash work and don't work for your favorite shooting situations.
One of my favorite exercises goes like this:
Set up a still-life tableau (or a compliant model) and put your camera on a tripod. Set the aperture to f/3.5 and allow the camera to pick a shutter speed. Take a picture. Then move the aperture to f/5.6 and allow the camera to pick the shutter speed, and take the picture. Do this for each aperture your lens allows. Don't zoom at all; just keep the camera on the tripod, focused on the same part of your picture. Then print them all out and write aperture and SS on them and pay attention to how the DOF changes.
Then do it again with shutter speed. For shutter speed, find some running water (even water from the faucet.) so you can see how the camera freezes movement or shows blurry movement as the shutter speed changes. Pick a shutter speed of 1/1000th or 1/500th of a sec and allow the camera to select the aperture and take a picture. Then change shutter speed to 1/250, then 1/125, then 1/60, etc, each time allowing the camera to pick the corresponding aperture, and each time keeping the camera focused on the same exact spot. When you print these out, you'll see how the shutter speed affects the movement in the photo.
I used to ask my photo students to do this and it REALLY helped them get aperture/shutter speed clear in their minds.
But don't give up! Just keep trying and trying, and also look for free articles and tutorials on the web. There are lots of great resources and I know you'll soon be loving that camera!