Can a polygragh test request help mw?

I am being prosecuted for a misdemeanor 2 in Allegheny County, PA, USA. I did not do this misdemeanor. What I did is either disorderly conduct or no crime. An off duty cop and 3 women who were passing me in a car have stated in the police report that they saw me do this misdemeanor 2. My 1st attorney told me that the cop who filed the charge (not the cop who was driving the car) was willing to do a plea bargain by which I would plead guilty to summary disorderly conduct. The attorney told me that the cop didn't want to finalize the deal that day of the preliminary hearing in city court, but a few months later in county court, to make sure I didn't get in any more trouble in the interim. This lawyer wanted substantially more money in order to continue to represent me at the formal arraignment, pretrial conference and at the trial date, when the deal was to be finalized. I obtained another lawyer who is representing me for less (so far). The assistant DA has indicated to this second lawyer that I never had a deal, and that neither the 3 women, the cop who was driving the car that they were in, nor the assistant DA will accept anything but a plea of guilty to the original misdemeanor 2 charge, not even a no contest plea, but after I plead guilty, he'll recommend me for the ARD program. I understand this program has substantial fees which I must pay, plus there might be an additional fine, and probation for 1 to 2 years. There is to be automatic expungement upon completion of the program and payment of all fees. If I go to trial, I could be acquitted or found guilty. If found guilty, the misdemeanor 2 will stay on my record for at least 10 years. I'll have to pay extra to have it expunged way in the future and also apply for it and check records myself or hire a lawyer again in the future. My questions are 1) Did the cop who filed the charge have authority to offer a plea deal of summary disorderly conduct? 2) Should I call a Pittsburgh police commander and ask to take a polygragh exam to give some indication that I did not do this misdemeanor 2? Should I write to the Allegheny County DA and ask if a polygragh test can persuade the DA or ADA to drop the charge or offer a plea deal with a summary charge? Do judges usually automatically believe the cop, especially with 3 other witnesses? Must witnesses, in PA law. be INDEPENDENT, that is , unable to be influenced by each other? This would usually involve them not knowing each other. The 4 witnesses were in a car together late at night. Either they mistook what they saw or they have lied and filed false police report. Should I go to trial or plead guilty and hope for ARD?