You're off to a good start! The modified version looks a little over-done to me, but you'll get more comfortable with PS with more use. Mostly, the colors are a bit saturated - adjusting it down a little might help. I do like the contrast adjustment though.

Two different light sources with very different color temperatures will always lead to bigger differences in an image than how your eye sees it. Incandescent and halogen is in the 2700-3100k range and daylight shade is probably closer to 8000k or higher. If it were me, I'd probably pick a white that was lit with the incandescent room light with the eyedropper in Photoshop's RAW converter.

I suppose you could adjust the blue saturation to lessen that effect (which looks fine to me) or do something a lot more complicated (which is beyond me!) if you really wanted it to look the same as the interior lighting. Like I'm getting at; sometimes less is more!