Your description of the DIL sounds like someone who is trying to gain control over everyone else. If she is not the center of attention, she uses punitive silence to gain attention. She is teaching your granddaughter that it is only okay to love her (the mother). If you don't show me your only love, I will ignore you, is the message. By doing this, the DIL gains control of everyone and thus everyone tiptoes around her bad behavior.
What can you do? Well, like the others said, you can't change another person's behavior. But you can change your reaction and thinking. Instead of getting upset inside and feeling in conflict or put down by the DIL, realize that she has some kind of "issue" that makes her need to be the center of attention. Try for compassion instead of anger.
Just like with an alcoholic who is using manipulation to control the family so they don't complain about his behavior, you can make sure the DIL experiences consequences of her actions, as best you can. For example, if she is not speaking to you, then you don't ask her what she wants for dinner, you don't go out of your way to keep her happy but you also don't get nasty with her. When she gets silent, you detach and stop caring how she is. Just live your life, focus on you and your granddaughter. Do not focus on the DIL's behavior.
Many on this site say look at it from the other person's perspective. Your son is not going to speak up but you can if you want to. He doesn't want the hate aimed at him so he's learned to be passive. Or perhaps, your son doesn't give her enough attention or show her love so she has figured out how to demand it. For some people, any attention, even bad, is better than none. You don't have to get in her face but when she is pouting, and thus controlling everyone else's behavior, you don't have to give up your power. You can matter of factly call it what it is, "Oh, Sue is mad at me again" but this has to be said without anger or criticism. Just like you might say the baby needs a diaper changed. Just matter of factly. Or "Go sit by mommy, she needs your love." Just call it what it is without being nasty or angry. You have to be the more mature person. DIL may just need more love, more positive interactions, some compliments.
It depends on what you want and how you feel about the manipulation. No matter what, changing your thoughts and reactions will change the dynamics of the situation for the better. Yet, once you change your behavior and detach from the emotional side of DIL's behavior, the walking on eggshells feelings you probably experience, she may escalate her manipulation and pouting type stuff. You will be tipping the balance of the scales back to a more healthier interaction/family dynamics and she will likely try to grab on to having it tipped in her favor or attention on her, etc. If she is just desperate for love, and is basically a nice person underneath, your kind actions and compliments may swing the dial. If she has a personality disorder, the manipulation is aimed for control of everyone so nothing you do short of strong boundary setting will really work.
