When you are in the hospital giving birth... your Husband should be the primary one to take care of her, AT HOME, when you are away.
Make sure he knows her routines... and KEEP her routines as normal.
I, wrote down for my Husband, everything about my daughter's routines prior when I was in the hospital for my son's birth. I was int the hospital for 3 days. I had had a c-section.
My daughter, was fine. My Husband did fine.
They called me on the phone to say good night, they visited me in the hospital as soon as it was allowed after I recovered, we bought my daughter some gifts for herself as a "big sister" and for her to bring for her new baby brother etc. I made sure to praise her... and she slept with my t-shirt etc.
I had never been away from my daughter either prior to my 2nd child's birth... but my daughter did real well.
Sure, Hubby will be with you at the birth. Mine was too. In that time, Grandma took care of her at home... and as soon as it was fine... after the birth, they came to visit me. But, after that... I would, have Hubby take care of your girl... at home, and spend a special time together.
I did not expect my Hubby to be at the hospital all the time nor all day... because I'd rather have him with my daughter, helping her... and being with her. They actually had fun together... and it was a nice bonding thing for them.
If your daughter is made to stay at Grandmas' for that whole time... she may feel left out, ignored, pushed to the side etc. I would think, staying home with Daddy, would be better. That way, she is a PART of you/Daddy/her new baby sibling... not out of the way at Grandma's.
All the best,
Susan