you shouldn't have to pay twice.
btw, why would a PCP be doing a PAP test? I don't know where you live. Here in N.Y, I've never heard of a PCP doing a PAP test ever.
Only a GYN Doc would do that
While understanding the authorization requirements is really your responsibility, many providers or their office staff will do some of the legwork as a courtesy to the patient. In this case, I'm not sure you have the case for an appeal with your insurer unless you actually think they denied this incorrectly, especially since it sounds like the error was in your PCP's lab (disclaimer - I'm not a physician or lawyer, and don't have all the facts about your issue).
Your best course of action might be talking with your PCP's office. You could ask that they reduce or even cover the $100, as you would expect that they work in partnership with you to ensure the care they are recommending is truly necessary and covered, especially in the case of 2 identical procedures in two weeks. You may also have a case that the lab should have been able to do what they needed with just one sample.
Either way, your best course of action is approaching your PCP's office, and asking them to work with you on this as part of a long-term phsycian-patient relationship.
Find more info at http://www.healthharbor.com, and perhaps post this question on that forum.