What is it called, in literature, when the author makes an evil character seem not so bad when he is nice to animals or children?

I think you are talking about "humanizing" a character. From a writing website"

"The best way to humanize a villain is simply to get away from thinking of him as *the villain.* Try not to categorize him. Try not to limit who he is because he is standing against your protagonist."

More information and hints here:

http://crimsonleague.com/2013/07/27/creative-writi...

Evil Characters with complexity are Round Characters not Flat Characters

There is nothing more depressing for me than to open a nice piece of fiction and find flat one-dimensional poster board like characters. It is boring to me to find an evil villain who looks hideous and acts dumb or a beautiful star with impeccable taste and a gorgeous attitude to boot and no change or important flaws throughout the entire story. I’ve seen bad storyline where the evil people act evil from the get go and heroes are completely handsome and kind, but I know it’s a bad idea. I’ve also seen extremely flat characters traipse in and disappear without a lick of importance to the story or any reason to be there. There are no bit players in your storyline and there are no completely flat people in real life. If you follow that one caveat it will not only take you a long way to making round characters, but it will help you to understand and promote the human condition.

An evil person must be shown with great empathy so that readers can get a flavor that they feel they are behaving in a virtuous way for very specific reasons, and however flawed those reasons may be.

The fact of the matter is though we want badly for evil people, even in our history, to be shown only as ugly or hideous in appearance and attitude, no one ever is completely, not even the worst people in our history, and everyone put their pants on in the morning. That same caveat is true of the virtuous. No saint didn’t have their flaws. Good story line shows the good and the bad and works toward showing attitude change in all characters from the start to the end of any story.

Your villains, antagonists, enemies (characters) need to be complex. I think complexity is about compassion and conflict. It’s too easy to write a drunk abusive father, a womanizing pimp or a violent killer. For them to become round characters — to avoid being FLAT — you’ve got to write something in them that brings out their humanity.