I have been the new baby in this scenario.
My sisters grandparents and aunt were always nice to me - we would see them at drop off and collection of my sister, as they were the intermediary between my mum and her ex. They weren't local which must have impacted the time spent together. They gave me cards and a bit of money at birthdays and xmas, but understandably would always give my sister more.
My aunt on my dad's side, who is more of a nan figure, treated me and my sister the same. She was local and we spent a fair bit of time with her, and my sister chose to call her auntie.
Looking back, I have no idea if my sisters family got upset or not. But I know it was the best outcome for me and my sister. It was OK for me to be treated differently by her family - they were nice but they weren't my family and never pretended to be. And nothing ever changed for me because this was the way it was since birth. But for my sister, who didn't get to live with both her parents, and had changes in life seeing our mum go through the divorce etc, it was important that she felt part of the new family unit my mum made with my dad.
Your grandchild is feeling part of that unit - she isn't any less your grandchild because other people are being nice to her and including her. Stop making this about you and your feelings and think about the impact on your grandchild if you got your way. It's sweet that your grandchild wants you to be involved with her new sibling, and shows that you aren't been spoken about as her 'old family' in the home - just make an excuse of the baby is too small to come to your house just now and she'll stop asking.