There is a difference in how my kids react to my parents and my MIL.
We only see my parents a few times a year. My kids love to be with them. My mom plays with them, reads to them, cooks with them, teaches them crafts. My dad tells them stories and jokes and tries to play games with them despite his physical limitations. They interact a lot with them and are both very encouraging and don't pressure my kids to do anything.
We see my MIL many times a week. My kids like to spend time with her, but... She watches them play and doesn't really do things with them. She is more of an observer. She is constantly telling them to dress warmer, read something to her, spell something for her, count this for her, stop jumping so much, to be careful, to put a hat on, to say I love you Grandma, or kiss her. She will offer them something to eat or drink over and over, even when they say no It never stops. They quickly lose patience with her and they often complain about things she does. They don't like to spend a lot of time extended periods of time with her.
Your daughter is only 3 and at that age kids do sometimes have a hard time with not having favorites. Our daughter was a total daddy's girl at that age and our son was a total mama's boy at that age. It's possible that she just relates better to one grandmother right now. That could be because of how they interact with your daughter or how much time she spends with them. It can seem that she is being hurtful, but at this age it probably isn't intentional. She will outgrow it as she gets older. Your mom will just need to be patient.