I know exactly how you feel as the last time I trimmed my older dogs claws she also jerked and I quicked her. And I was only clipping a short amount at a time. I do as zoebess suggested and clip a smaller amount but at closer times....
Anyways, I wanted to tell you that you can use cornstarch to stop the bleeding. It works in the same way as a styptic pen. Most kitchens always have cornstarch...