I agree with everyone else - stick to your guns on this one mommy! I don't have kids, but I am a child (all grown up now) of a mom who would not have hesitated to do this. And, I have to say, when it comes time to teaching lessons and punishment you have to take away something that is meaningful. Believe me, they will appreciate the lessons you have taught them someday. I really do appreciate what my parents did for me - though, like your daughters, there were tears and some anger in those moments when I was being punished.
Additionally, how lucky for your daughters to have a mom who cares and loves them so much. Being a parent is a difficult job - I can't even begin to imagine. I pray that I will have your strength and compassion when it is my time to be a mother.