I have 11 grandchildren and have been blessed to be at each of their births, except the last two, and helped out afterwards. My Mother always came and if I remember correctly, at times both my Mother and MIL came... they just took turns.
I have heard from others or from young mothers themselves that they don't want their family or siblings in the room for delivery. See, I am blessed because even my DIL wanted me. Those are special moments. There is a way to stay out of their way while you are staying with them. Usually, that type of help is very welcome. I hope it all works out for you. Congratulations on the birth of your grandchild! It is such a blessing to be a Grandma...