I've posted this in Parenting as well but I though you emotionally literate lot might have some ideas?
My MIL is quite an odd and evil person. She sometimes says things to our dd which are designed to be divisive eg 'Your mummy's wicked isn't she?', 'Your daddy was so rough with you then, granny would be rough with you' (we are neither rough nor wicked btw :) )
She also sometimes says things which are just plain old evil: 'We'll all hate you when you're 15' and her classic 'When mummy has a new baby she'll forget all about you'. 
DD is 15 mo so we've mostly been ignoring on the basis that it's really not good for dd to hear a great big huge row which is what happens when MIL feels threatened (and on the basis that actually the comments are directed at us and fundamentally we don't give a shit) but obviously she'll start to fully understand soon. So the question is what does dd need to hear us respond with? Is it enough to say 'I'm not wicked MIL'? Or 'We'll never hate you darling'? or does she need to hear us be firm about not saying things like that?
If dh or I confront MIL directly it will lead to 'Well we don't want to see you then'. And then the question is whether a relationship with your granny who can sometimes say things which are really nasty is better than none at all...