In NifSkope, for whichever part of the Mesh that you are trying to brighten, look under the "Editable Mesh", and look at the "NiMaterialProperty". Click on that, and then go to your "Block Details". You'll see:
You'll see a Color Wheel followed by a # and a string of 6 Numbers/Letters. If those read "#ffffff" then that's as bright as it will go (I think). If it's not, click on those Numbers/Letters, and change them all to "1.000". There may be other ways to do this, but this is how I've done it in the past.