One of my nursing jobs
was, well, toxic! We had a clique, and if you were in it OR didn't do anything to upset them/ask any questions, things were good. If they didn't like you, you asked too many questions, upset them or thought for yourself, or whatever - they not only talked about you, they complained to management about you and worked on getting rid of the people they didn't like. One of their "tricks" was to send new staff just off orientation to nights (where the nurse educator and nurse manager weren't around to evaluate the situation themsleves) and the nights group would either make stuff up or find ways they catch you not being 100% right...and it get exaggerated and reported (the exaggerated version of events).
My advice would be to not give up. There is something better out there. Nothing will be perfect, but there will be something that is a much better fit for you that will come along when you least expect it. I wasn't 100% looking to leave my second job as it was leaps and bounds better than my first, but I had the chance to move closer to family and I jumped on it. I LOVE my current job. Our educators are great, our managers and assistant managers are great. Our charge nurses are pretty great too. There are still "days" as every job has bad days, but the good outnumbers the bad by far.
When I was asked why I left my first job, in interviews for other jobs - I calmly explained why I felt it was unsafe for staff and patients. I didn't trash my former employer, just identified several flaws. There were positives too, I learned a lot about nursing, I learned so much from some of my patients/have amazing stories about how I positively affected them and more importantly, I learned who I don't want to become in my career. It's a hard lesson to learn, and it sounds like you (original poster) are well on your way to learning it yourself.
I would be honest about having worked at XYZ - depending on how they conduct background checks, they will almost certainly find it. Many hospitals state that omissions are considered lies and any lies/falsification on applications can be grounds for withdrawal of offers and/or dismissal if they later find out you lied. And there is so much (undoubtedly) that you learned, give yourself credit!
And, I agree with a previous poster, if my union rep had said they had grounds to fight the dismissal, I probably would have let them fight for me, if for no other reason than to clear my name. But you have to make the best choice for you, and that's not for me to decide.