T.S.
It's very normal. I've had three kids, and it was hard leaving each of them for the first time (and many more after that). Leave them with her grandparents and aunt. Some of it's for them, some of it's for you, but a lot of it will be for her. It's much easier to help her become comfortable with other people now than when she is older. Look at how she will act when she actually must leave you (school) and how it will be difficult unless she is used to it.
My 4 year old never wanted to go to anyone else when he was a baby. I didn't push it because I didn't want to upset him. Now we are getting ready for kindergarten, and while he's excited, I know it's going to be traumatic for him. So we are working really hard at getting him used to different people and situations before that day happens. I just wished we would have addressed this at a much younger age.