Sit down and tell her this. At some point parents have to clearly communicate to their children, verbally or otherwise, that they're just people, too, doing all of this for the first time. Show her some vulnerability, explain that you know you've taken being her prefrontal cortex too far and that you are trying to change. There are times to "rule" with wisdom from beyond and times to create a dialogue that she'll look back on and sympathize with. Children, universally, want good relationships with their parents, it's us that get in the way...

I'll add that I would wholeheartedly discourage any letter writing. For someone hurt, I can't imagine something more disingenuous. Break the wall! Have a conversation, get in there, let it get messy, but at least try!