@Wen: I am not a CSS expert and I certainly don’t have CSS code to explain how I do it. What I have noticed is that if I click on a blockquote the size of the cursor is bigger, and you cannot move it to the end of the line. However, if you then e.g. click the backspace key, the cursor does start from the end of the line.
If you want to edit in the middle of a sentence in a blockquote, or in a sentence that has e.g. a pair of * around a part of the sentence, the trick is to temporarily remove those (or the > in the case of a blockquote), do your edit, then put the formatting back.
It sounds like a lot work, and at first it is, but when you get the hang of it, it is not so bad.