I used to cry my head off when I had to leave my grandparents.
The last time I did that I was ummmmm, 33 years old.
I adored my grandmother and she was quite elderly. I lost it when she said, "Honey, this will be the last time I see you in THIS life again, but remember, I'll always be with you".
My kids cried when they were little about leaving my own mother. My son gets the sniffles when he has to leave his sister. She's 25 and has her own home and child now. He's only 16 and loves going to stay with her. He misses her.
I think it's pretty typical, especially with little kids. They'd like to have everyone they love with them all the time.
Just comfort your granddaughter and let her know you'll be back to see her soon.
Some parents feel terribly bad when their little ones behave this way. I wouldn't say anything to make your son and baby's mom worry about it.
The little one loves you and doesn't want you to go.
She'll be all right.
Best wishes.