Should I have to defend my choice to not invite my Grandmother to my baby shower?

I wrote my list of people to invite to my shower and gave it to my MIL. She did question the fact that I had no biological family on the list but I just said yes it was intentional and she went on her way. My mother is an obscene alcoholic and my sister can only make it down once and I would rather that be for the birth. But now the lady I have lived with and my aunt and step grandmother are all asking me why my moms mother hasn't received an invitation. They all know my grandmother constantly says awful things about me like that I just post pictures online that make me look thinner than I am or that I'm "not as smart as everyone puts me off to be and one day everyone will be disappointed in me". Even these things I ignore on a regular basis and while I don't choose to spend much time with her I have always previously been nice and invited her to gatherings and such. Then one day my sister had her on speaker phone and my sister was explaining that I got a new job. My grandmother heard I made more than my sister and said "oh well honey Rachael will never be able to do what you can. Create beautiful babies." And that was when I realized that I can handle her being mean to me. But this is my first child that isn't even born yet and I cannot be civil with someone who says something like that about my child before it is even born. Everyone puts it off as that is just how my grandmother is and that's nice and all but I don't want her there. She used to say things like this to me as a child and I won't have anyone degrading my child. I shouldn't have to keep having discussions with people trying to convince me to let her go, should I?