DS1 has (had) clinically diagnosed night terrors. His paediatric consultant and parasomnias consultant described his as among the most severe they had ever encountered.
Here's the advice we were given. It's completely counter-intuitive, but it works. It has reduced DS1's night terrors from half a dozen per night to perhaps two or three per week.
Caveat: it only works for genuine night-terrors, and is inappropriate for nightmares. If your DD remembers her nighttime experiences the next day then you are possibly not dealing with true night terrors, but something else.
Disclaimer: I am not an expert in sleep disorders, only in DS1!
Here's the advice. Do not disturb DD during a night terror, or try and stop the night terror once one has started. The o my time you should even so much as touch her is if she is in imminent danger of hurting herself e.g. falling out of bed. Don't talk to her, stroke her, make eye contact, put her cuddly toys near her - nothing. You can be in the same room as her, but don't make contact at all.
It's incredibly hard. Because they look like they're suffering so much. But, in true night terrors, the reality is that they know nothing about what is happening.
The latest sleep studies suggest that night terrors are caused when the sufferer's brain is trying to go from a deep sleep state to a light sleep state, and doesn't make it for some reason. The night terror is the physical manifestation of the brain's attempt to make the transition.
By interrupting the night terror you stop your DD's sleep transition that night (which is very confusing and upsetting for her in itself) and stop her brain having the opportunity to learn how to make the transition for itself, thus guaranteeing that she'll get night terrors the next night, and the next, and the next...
We felt terrible when we were given this advice - like you, we'd been rousing DS1, unaware we were making his problems worse.
Once we implemented the new system of letting each night terror take its course there was an immediate improvement.
Finally, we found it helpful to keep DS1 as cold as possible at night. No nightwear, sheet when you'd expect a summer duvet, etc etc. There's no scientific evidence that this helps, but it seemed to for us.
Good luck.