Divorced Parents and Wedding Invitations!?

My fiance's mom and dad are divorced. He cheated on his mom years ago and left the family to marry someone half his age. My fiance is somewhat close to his dad, he will definitely be at the wedding. We do NOT want the new wife there, too much of a risk and we hardly know her anyways. My question is: My fiance has already decided to ask his dad not to bring the new wife. Do I put her name on the invitation to be polite? haha, or has all politeness already gone out the window with this mini-drama?!