Its not ridiculous to have the blankie for sleeping. However asking for it every hour is, and driving to Grandma's house to get it is as well.
I'd start by saying that the blankie needs to stay in her bed at all times, she's allowed to have it only at naps and bed time. Set a firm boundary about not whining about not having it the second she wants it. Decide what you think is a fair consequence for continued whining, and when she starts give her a warning, and then if she persists institute the consequence. Be firm and consistent. You might need to make the consequence worse if it doesn't seem to make an impact. Lastly, if she still is making a huge deal over it, let her know that the blankie will be staying with you for a day and she will have to live without it because she cannot stop whining/asking for it. Then just prepare yourself for her to throw an absolute fit, but DO NOT GIVE IN!!! She can have it back after that day, but she'll have a new respect for you, that you follow through. Buy some ear plugs if you have to. (my husband finds them very helpful with infant crying).
Kids need to be prepared to live with disappointments, and its our job as parents to prepare them for that. This is just one area (leaving it behind at Grandma's) where we can teach them.
Best wishes!