I think resigning from your job is an overly dramatic response to the situation. Be clear and honest about the situation and what you can and can't do, but there's no need to jump to that step. If they decide that they no longer want you employed it will be clear.
As I explained, resigning was a bit so that they would have time to hire someone else to cover the shift (the non-dramatic part) and a bit to stop them from being able to fire me because I was already quitting kind of thing (only dramatic in the sense that I was thinking they would fire me over my first write up). Otherwise, I don't understand why you think it is dramatic? Could you please explain?
Dramatic in that it something that is over the top, perhaps quite striking and effective but possibly disproportionate to the situation.
I do understand your reasoning in that maybe it would be best for them to have the role free to full - it's entirely possible that this is a solution that would suit them. But it's equally possible that they'd go "Oh no! We thought we were just trying to cover one shift and now she's QUITTING?" Based on what you've posted re the interaction so far, it just isn't clear what they'd prefer. So while offering to resign could be a nice gesture if you think it will help solve the problem, it really doesn't seem necessary at this stage for you to outright resign. You're jumping from A to C and skipping B. If that makes sense. 
Hence dramatic as in over the top. (Not in a dramatic, childish way if that's how you took it - certainly didn't mean to imply that!)
It makes a lot of sense, thanks for explaining! In that way, I actually agree with you. For whatever the reason, these things didn't cross my mind...probably because I'm so ticked at the other server for going and getting football tickets when she found out she couldn't work for me that morning due to overtime.
Yes, TootsNYC, my mean side, too; so far, I've only told it to people not at the restaurant, ie my boyfriend and mom. You want to know what the worst part is? She's my best friend. I really need to sit down and talk with her once I cool off a little...I'm going to go with she forgets I'm taking the LSAT that day...at least I hope.
Also, to give a bit better perspective, this is the restaurant in a hotel that is only open for breakfast, thus she and I are the only two servers. Her being my best friend is also why I trusted her to cover the shift without requesting the day off (which is usually OK where I work, as long as you let the supervisor know (which I did)....but I'm never doing that again.)
I'm not really worried about the write up, I guess, I'm worried about how pissed off people will be at me because I left them in a lurch simply because my best friend and I are the only two servers.
