Which is correct?

"her and me" is correct. Both "her" and "me" are objective pronouns, and are correctly used as the object of the sentence. You can test the rule of which pronoun case to use by using only one pronoun and seeing if it sounds right:

"Please send all emails to me."

"Please send all emails to her."

"her and me" might sound awkward because so many of us have had it beaten into our heads that "she and I" is always correct. This is not the case-- "she" and "I" are subjective case pronouns, and should only be used as the subject of a sentence:

"She and I will receive all the emails."

"She will receive all the emails."

"I will receive all the emails."

I tend to perfer writing our names in a situation such as this:

Please address all emails to both Susan and I.

Mark