J.F.
I'd say have your husband invite her over and sit down the three of you and talk about it. She needs to hear it from him, too. I'd also suggest finding someone else to watch your daughter while you're out so that your mother-in-law gets the picture. I had to do that with mine.
Does Grandma treat your sister-in-law's kids the same? Is there a reason she's saying your daughter is spoiled? From the sounds of it, both of them are out of line (I may be way off base here, but it perturbs me when people attack someone else's parenting without all the details). Does your sister-in-law know about Grandma over-stepping her bounds? There may just be a lack of communication/understanding between the family.
Lastly, if Grandma is purposely causing jealousy issues for the grandkids, that's not a healthy relationship, and she needs to stop. The kids will grow up resenting their cousins, and that's not what family is about. Have a chat with her about this, and if she doesn't change her behavior, find another means of childcare.
On to your daughter. My son did the same thing. When I asked his doctor, she said he was testing me to see how much it would take for me to say I didn't love him anymore. Two year olds push the limits to see what they are. It confuses them, sometimes, when they find out love is boundless. When my son would throw fits I'd just tell him "even though you don't like me, I still love you" or "it's ok if you don't want to share that toy, but if you want to play with me later, I'll be over here". Sometimes it would take him an hour, sometimes only a minute, and he'd be in my lap playing again. He just needed to know where he stood, I guess.
Good luck on this. Issues with the in-laws are always tough ones. Hang in there, and let us know how it goes. :)