What if I don't let my daughter open all of her birthday presents?
Why would you want to do that to her?
I'm saving some of it for later.
It is too early for your daughter to open all of her birthday gifts, but she will not be happy if you make her wait. Why not just let her open them all later, that way she won't have any anxiety about having to wait after getting started. She will just have to abide by the rules because you are the parent.
She's going to hate me forever.
She will be upset, but it won't last forever. If these are your rules then you are the parent and can enforce them.