Okay...honest opinion here.
I am a costume designer as well as a dancer-and personally I would AVOID the bright red with the lime green. Red is the opposite on the color wheel of TRUE GREEN-as in Crayola green, and not lime. Lime green is more a mixture of green and yellow-and a loud version at that, so red isn't as complimentary.
You have adjoining hardwood floors, and you have a lot of beige/sand tones around as well. I would personally go with CREAM walls. Not white, but very light off white-then bring the sand/beige sort of tones in with curtains and maybe toss pillows and the like. Bring in darker brown tones with picture frames, maybe in some of the furniture, and so forth. I don't think the beige/sand walls AND curtains together would have the impact that cream walls/brown/tan curtains would have.
Also, you are going to bring in dashes of the lime green in as well, in other small areas....a funky looking vase...a throw pillow or two...small dashes here and there. The off white, and the browns are going to be your main tones in the room, the lime green the accent color-and then here and there in very small doses for a splash of color accent-I woul recommend ORANGE. Yes, Brady Bunch orange. Trust me on this one.