Problem with my gf and baby?

My gf of 4 years has a problem with letting my mother see my 2 month year old daughter. She doesnt want her told her or see her because she thinks she obessed with being a grandmother. When my mother held her today i went back up to get her and she was changing her diaper. I got her and my gf was jealous and said i dont want her changing her diaper i wanted to do it. She then said i dont want her now your mother can be her new mommy. We have been at my mothers house for almost 2 weeks and my mother has only held my daughter 3 times. When my gf's mother seen my daughter she wanted her mom to hold her everyday even though i wasnt ok with it. But i still let her mother hold her. My baby needs all the love she can get. So how do i make my gf be nicer to my mother. All my mother wants to do is hold her granddaughter is that to much to ask for.