I can empathise with your feelings. Sometimes you might feel guilty about feeling as you do. It's jealousy, born of insecurity, and it really really hurts. Ask me how I know: I'm the queen of jealousy, however illogical and unreasonable I might know it is.
It makes you feel guilty because she's your mum and you don't feel you can assert yourself over her for fear of looking childish and betraying your feelings. So you're stuck! Shame keeps you that way.
I wonder how close you are to your mum and whether you can arrange to have a chat with her about how bad you're feeling. She probably has no idea and would be mortified. It takes courage to admit to feelings which are uncomfortable but I believe it's worth taking the risk.
You could say that you've been looking forward to being a grandparent for so long, but your feelings are that she is taking more of a grandparent role than you are and though you are very happy that she has such a lovely relationship with your DD and GC, you are feeling rather sidelined and it's making you feel sad and left out. Ask her for help in this; say you'd like you both to find a way to move forwards so you feel more like a grandmother and less like an also-ran when you are all together.
I am feeling similarly jealous, though in my case I KNOW I am being unreasonable. I've seen on Facebook that my DD posted that she, her partner and her baby daughter) had a lovely happy day with my father, stepmum, brother and my brother's family. Nothing odd about that, is there? So why did I get a terrible pang of sadness and jealousy? I thought they were only seeing my dad and stepmum and the thought that so many of the family were getting together without me and DH makes me feel like a child who's not been invited to a birthday party. I can hear some gransnetters mutter, 'FFS, woman, get over it and grow up!' but it still hurts even though I know it's unreasonable.
I know that with me it's insecurity leading to these painful feelings, but it wouldn't be reasonable of me to voice them. Your situation is different - and I think you could well feel some relief to admit to your mum how you are feeling and enlist her support and compassion in helping you to sort this out. Good luck!