I had the same problem with a 3D printable model I’m doing for a client right now. I wrote a blog about it on my Ko-fi Page
It might be the result of being in edge or vertex mode during the unwrap, but maybe not. I’ll have to play with it still.
But basically there are likely some floating faces/polys that may be stuck inside other UV islands. Your mesh is split up into islands when it’s unwrapped. Sometimes the Unwrap process will throw some of your individual polys out into their own islands. Sometimes those polys you want to paint brown will be thrown into the same island as a white so they get overlapped and stay white.
If you hover your cursor over each island and hit your ‘L’ key to select all your visible islands, then hit Ctrl>I to invert the selection, the floating polys will be more visible and you can just hit '‘G’ and move them out of the UV square, then find the ones you want brown and move them into the brown islands and vice versa for the white. Try that and see if it helps.
I had to break up my mesh into 5 parts because doing a UV Unwrap gave me dozens if islands and this issue was getting ridiculous.
I figured if I chose sections of my mesh that didn’t for, say, cylinders, where my mesh would get distorted, I could get more even flow. So to fix it I would first make sure selection in edit mode was on faces, not vertices or edges, otherwise you don’t select the entire face and get edges dangling off the edges of your mesh.
I would select a part of the dog that would be most flat and have the least protruding parts, so for example I would cut the cylinder of the front leg in half up-and-down so it would unwrap more flat, then unwrap what I selected, hide it, then when I selected the next bunch of polys that would have been connected to the first selection, I would hit Ctrl>+ a couple times so the selection would overlap into previous selection so ‘no polys left behind’ in the unwrapping process.
I explain it better, and with pictures, on my Ko-fi Page so check there if this doesn’t make sense. Good luck and let me know if it worked 
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