(2) is correct and has the meaning that you describe. (1) would be wrong in most contexts. I suppose it could imply that the speaker has been having a romantic relationship with Peter, but that this finished ten days ago.
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Laborious"I have not been seeing Peter for ten days". Could that mean that the speaker has not met/has not been meeting Peter for ten days?"seeing" is understood here to mean meeting regularly. It could refer to a series of romantic liaisons (as I mentioned) or possibly a series of appointments, e.g. with a therapist or counsellor or something. One sligh