Hi N.,
Don't take this as a reflection of your parenting because it really isn't. It's obvious that you care and that you're trying your best. However, I can certaintly understand your frustration.
My recommendations would be similar to that of the other moms (and an extension to what you're already doing). First, change the rule at home about telling you that she's going to the bathroom (although I understand why you're currently doing that because I'm going through that with my son). You may even want to explain that your changing it so that she can practice what it's like at school. Once she stops having problems at school, you can go back to the reward system you currently have where she gets the marble if she doesn't tell you.
Your idea about coming up with a code that she can use with the teacher is a good one. However, since that hasn't completely done the trick, I would ask the teacher if she would periodically and discreetly (or using the code) ask your daughter to go use the bathroom preemptively (like maybe every two hours). Basically like all of us moms had to do when first potty training our little ones.
Eventually your daughter will get used to going to the bathroom on her own in a strange place. Your teacher will find that she probably doesn't need to keep asking her. Perhaps the teacher can work out a reward system of her own to encourage your daughter to ask. Right now, she's so used to having an accident that it's probably not traumatic for her. However, once she stops having the accidents, she probably won't revert back.
And by the way, I think your reaction of getting angry with her is normal. If she doesn't think it bothers anyone, then why would she stop doing it? You're making sure to regularly use positive reenforcement and I think it's healthy to every now and then balance it out with a little negative too. So don't beat yourself up - it has to get better some time, right?