S.R.
My son, 20 months, was really whiney with me, but not my husband who stays home with him most days. I came to realize that he was whiney because I put up with it. When he was crying after being told no or because he wanted something he couldn't have (like being picked up), I'd wouldn't give in to his demand, but I would give him attention. I didn't want to hear him crying. When I stopped giving him attention and made it clear that his whining was bad and wasn't going to get him what he wanted, he stopped. Tone of voice was very important- I would say "no, I'm not picking you up right now" in a very firm way and that was it. No more explaining, no more trying to get him to cheer up or distract him. If he crumples into a little ball of pathetic mush on the floor at my feet, I'd ignore him. In fact, I made a point of leaving the room for a minute. It was very hard, but it didn't take long and he stopped. When I tell him no now, he might protest for all of 3 seconds and then he's fine. He knows that no means no with me.
This is up to Grandma. She needs to not give in to the crying- afterall, why would your daughter stop if she gets what she wants that way? and even negative attention is attention, which kids crave. Grandma needs to not pick her up on demand and be firm about telling her to stop. She'll get the message, but will Grandma? My mom spoils my kid rotten, so good luck to ya on that!