Absolutely agree nursery are being neglectful – leaving a child clearly wet or soiled is unacceptable. You could try pushing this angle with the manager, or even report them for it, particularly as it's not just your child you've seen wet, but that's obviously a fairly dramatic step.
I would also agree that supporting toilet training, within limits, is absolutely part of a nursery's job, and I don't see how a group reminder to use the toilet every couple of hours is so impossibly onerous. Even DD would ignore a general reminder, a competent nursery should be able to cope with the fact that this specific child needs to be taken to the toilet at the general reminder times – and it's not exactly a huge amount of extra work if there are a few going at that point anyhow. Do your nursery do group reminders at all?
In terms of helping it click for DD, you mention fear at one point. Can she explain what she's frightened of? Or agree/disagree if you suggest things it might be?
The flip side of rewarding going on her own is generally trying to make having an accident maximally inconvenient for her (at home, I mean). When she has an accident, do you have her get her own wet things off, clean her legs, put wet stuff where it goes, wash hands, get her own dry things and put them on? I also point out this takes a long time and it would be faster to get the wee in the toilet (just sort of factually, or sympathetically if they're clearly anxious to get back to playing, not a lecture).