Will it hurt our rabbit if we calm her down and to then hold her up by the scruff of her neck? We've done it before; she seemed squirmy at first but then she calmed down when we held her up by the scruff of her neck. Does it affect our rabbit in any way if we do it. How and how will it affect her in future life?
A rabbit should not picked up by the scruff of the neck. Occasionally you will see people grasp the scruff and support the body, this is usually to keep them from jumping out of your arms and hurting themselves. In no case should the rabbit be supported by only the scruff of the neck, they are not cats and can be permanently injured.
For safer methods of hypnotizing a holding a rabbit for care see How do I trance my rabbit? or What is a "bunny burrito" and when would I use it?