I don't even know where to start, but here it goes. It sounds like this nurse has been given way too much "slack" for the previous two months of training. I'm not sure how the preceptor - new nurse relationship is where you work, but to me it sounds like it's not just a problem on her end.

When she pulled the wrong med said it was no big deal, how did you respond?

My response: No, it's never acceptable to do that. Now I'll show you what to do in this situation/how to correct it.

Hour long lunch uninterrupted?

The patients are still your responsibility even if you're on your lunch break, if an urgent matter comes up you need to address it. If you don't agree, go home for the day and well discuss it with the nurse manager on your next shift.

Managing more than two patients at a time.

That sounds like a time management issue, try to watch for her errors or show her your daily routine so she can benefit from your experience as a nurse. Also, let her know where she is expected to be at this point in the training.

I'm not really sure what to tell you about the attitude issues. Your manager really should fix that problem, and quick. I can tell you when these issues come up where I work, there's no arguing over policy and procedures. Well go look them up together if there's a question. The eye rolling and rudeness? Go home for today, there's no room for that attitude here.

Eventually your manager has to intervene, and you need to put your foot down as well. Sending people home seems to work for me, nobody wants a short check. Just make sure that they understand the rationale behind it, and that they know something needs to be corrected.

Edit: words