I hope this message finds you well, present circumstances excluded. My name is XXXXX XXXXX I am an attorney with over 10 years experience in dealing with employment law matters, including drug test information. It is an honor to be able to assist you with this matter. I will answer your questions in the order in which they appear.
Am I able to take the company to court for defaming my name? Unfortunately, probably not on defamation grounds. To win a defamation suit, you must show that there was a false statement made about you that other third parties could hear, that the speaker knew to be false, or had reason to believe was false, and that you received harm as a result. The catchy issue here will be "false or had reason to believe that they knew it could be false". It is a failed drug screen and you are right that this is a very common false positive. However, the mass-spec machine that runs the test sees them as the same thing. Therefore, defamation would be hard to prove.
You may be able to have an injunction issued by a court which would preclude the necessity for you to adhere to the provisions of the "last chance agreement". In that case, you would only have to prove that this action can or will cause irreparable harm to you and that there is no other avenue of recourse. If you are wanting to go the court route, that is certainly something to think about. My legal opinion is that a suit for defamation, or the like, would probably be unsuccessful, but a filing for injunctive relief has a very good chance of succeeding.
Would the results on this test be able to determine this was cough and cold medication and not an illicit drug?
Probably not. You were administered a very generic and cheap broad test. It is unlikely that it would be able to tell the difference in a cold medication and other amphetamines. If they saved a sample, then they could conceivably run a more specific mass spectrum test and differentiate. Those test are expensive and therefore, even if they did save a sample, it is unlikely they would retest for that purpose.
Moving forward, I would recommend that you either immediately file for injunctive relief in an attempt to have this determination thrown out, or in the alternative (and certainly the path of least resistance), continue to work with your union rep in attempting to resolve this issue without litigation, even if it means submitting to a few test in the lag period before reaching a rational and pragmatic agreement with your employer. There really is no better or worse way. The first way may yield quicker results, but at the expense of further damage to your relationship with your employer...the later may mean taking test in the mean time, but better preserving your relationships with the employer moving forward.
Let me know if you have any additional questions or concerns!