What do you call a bear with absolutely no teeth?

When you're with me, I've always got that wet hairstyle. I glide across the floor, my movements clean and directed. After we're done the space is wet for awhile. And with a thorough wringing I am subjected.

I turn the rational into the insane, for reasons inane. If you don't keep me in check, your relationship I will wreck. Known as the monster with eyes of green, the only emotion I bring is suffering.

I have three feet, but no arms and no legs. What am I?

I am a mixture of different genetics, from a small mutation that makes two different color patterns, to a mythological beast with parts of several different species.