Denise,
I don't think there are any specific settings for refine edge that work on everything....you have to experiment with the feathering and other controls almost on each image to see what works best. One thing I would suggest (if you haven't done so already) you download a trial version of Topaz Remask. With some practice it is possible to do some very fancy selections, including hair. I believe there is a YouTube Video on the process.
On your recent image of Buddy, the main thing that stands out is the bottom of the image because the texture should not be running vertical there. That is what makes it look unnatural to me. Also the top edge of his left leg needs some work.. it looks like he has 2 front legs
I think you should continue to work on the process and you will conquer it. Each image, however, will take some time to process.