Well it doesn't sound over the top or dramatic to me. I can totally understand, Everyone is different, maybe you and I are over protective worried mumma bears, but you know what? Its just how I am. I don't 'have' to leave my kids anywhere so I don't if it doesn't feel right. Some people don't have that luxury of choice.
By the time she has to go to kinder, she'll be able to communicate and tell people what she feels and needs. It's so much easier leaving them when they are a little more independent. ( as I am just now discovering. )
Right now you are her world and protector. It's hard to find someone to understand her and care for her in the same way you do.