I know very little about digital, but if this were film I'd say that the first pic is getting flash only light (electronic flash is blue) and that the second pic is getting more available light from the Xmas lights and room lights (tungsten lights are orange).
Typically when I want to lose the blue cast of the flash I slow down the shutter so that the warmer room light will expose some; the slower the shutter the more orange it gets. You as the photographer must correct the camera as the camera knows only the quantity of light, not color of light. With film this can be done with a filter or in the lab (sometimes). With digital I think it's done by adjusting white balance, although it also could be done with filters or in Adobe PS (so you should still be able to correct for some of the cast).
Along with this you need to know how your meter operates even if you are working on full auto. Do you have different meter modes? I'll assume these were taken on matrix-mode which measures the light on the entire image. The meter saw a whole bunch of light colored wall, and gave you the setting to take a nice middle gray pic of the wall, which means it underexposed making the pics darker (I'd say the walls are at least three stops brighter than middle gray, so even though the camera tends to give stuff in the center of the image more attention, the large area of white wall throws off the average).
You need to either get in close to your subject or switch to spot meter, and meter only the important stuff. Manually set your camera to the recommended settings and then you can back up (but actually, take a few pics when you are up close). Or you could buy a 18% gray card and meter off of that.
Also, front lighting, unless done with finess, reduces form and texture and isn't particularly flattering for most folks. It also tends to look "snap-shotty", because most pro portraits will use some sort of side lighting and point-n-shoots all have horrendous front lighting. Try bouncing the flash off the ceiling or look into getting a flash cord so you can hold the flash off to the side.
And finally, YOU'RE SHOOTING DIGITAL!! You are getting instant feedback about your results and it only costs you battery juice to take a zillion pics. Start shooting and you'll figure it out. Your assignment is to fill your memory card everyday.