You don't say how old your daughter is so...I'm assuming she is in her 20s and on her own?
Don't be so hard on yourself. From what you've written, her behavior has pushed you to the breaking point. We're all guilty of lashing out at some point in our lives when we're hurt and/or angry. Consider sending along a follow-up email saying you regretted writing that you threatened to hit her. Without knowing your full situation, I'll say this --- You could tell her that as her mother, you'll always love her and that you hope that at some point your relationship will change for the better.
Your daughter needs to grow up. With some kids, once they mature, they are aware of the pain they caused and will reach out to make amends. When she grows up, if she extends an olive branch, take it.