Is this the correct way of handling this?

I recieved a phone call from my manager, who, once again, told me to watch my mouth. This is has become a favorite topic of hers since the incident I related in the thread "another nurse flat told a lie about me". This time, she said another agency nurse complained about me, saying I said we were half way thtough report. In explaination, I was called at the last minute to go to a new facility for me, 62 miles away. I was relieved to have the work and went, with no knowlegde from the agency as to where I was to work (I was told Med Surg or Er or ICU, they would tell me when I got there.) As the drive takes an hour and a half to get there, they were told I would be late. However, the agency did not tell me how late I would actually be, the shift started at 1730 and they didn't even call me until 1630. I got there, late, and they sent me to med surg. I was half way through report when another nurse from my agency shows up and got very upset that I was there. She stated SHE was supposed to work Med surg, I was to go to ER, and be pulled back to med sur if ICU got a patient, which She would take , that Connie(Our Manager) said so. She was very irrate in both her speech and body language. Having no dog in the race, and just being glad to work I said fine. The shift supervisor said she was half way through giving report to me, could the other girl not go to ER because it would be better. I told the girl that I didn't care, either way was fine with me. It developed that she had more ER experience that me, so I stayed, she went. As it was my first time there, I was amendable to anything anyone came up with. I would have swept floors.The shift super then tells me that that Nurse wouldn't have gotten pulled to the ICU anyway as SHE was the ICU Nurse, if we got a patient to ICU, I would take her med surg patients, I said fine by me, I'm here to work. Good shift, no problems. Then today , I get the phone call from the Manager of my agency about the other Nurse saying I said we here half way through report. I didn't, oh well. I figure anytime anyone says anything, it's going to me my fault from now on. In light of this, I have decided to ask for a meeting with the Manager, the other Nurse and myself and I am going to face her and relate what actually happened. Then I am going to wait, applying for new positions in the mean time with other agencies, and then go over to another agency and work as I am sick of this. What do you think?