By not reacting to her cold shoulder treatment you will, in essence, be eliminating all the enjoyment your wife may be deriving from it. By employing this new countermove, the scenario will likely change. Once your wife begins to talk to you, you can gently and calmly apologize for saying something that hurt her feelings. And temporarily at least, leave it at that.
When your wife is calm and in a good mood, invite her to sit down for a discussion. Tell her how much you love her and how special she is. Inform her that you sometimes feel (emphasize your feelings often) that she gets upset at things you say, but that you never mean to hurt her and that you are not sure why she takes your words out of context.
Do not bring your mother-in-law into the conversation.
Both of you should devise a secret word, one that you say when you feel that your wife is overreacting to something and one that she says when she takes offense at something you said. This will help both of you realize that something is amiss and thus give you a chance to nip the impending dispute in the bud.
I hope that my advice helps you. Hatzlachah!