Hello,
I'm not entirely sure how to fix the built-in screen time function for Apple, unfortunately it has been very buggy/unreliable since its implementation.
That being said, I can offer an alternative: ScreenZen (https://apps.apple.com/au/app/screenzen-screen-time-control/id1541027222). It's a free app on the appstore, and I've been using it for quite some time on all my devices (iPad, iPhone, Mac). I've found it to be a lot less buggy, and it provides options for how an app can be unlocked, for example, you can make it such that a certain number of mathematics questions have to be answered in order to unlock an application.
The significant difference is that it has to be downloaded on the device that you want to choose restrictions for, meaning that there is a potential for your daughter to change the settings or just delete it entirely.
For the first issue, I do know that there is a setting where you can 'lock' any changes with a passcode that only you would know (see first image).
For the second issue, I could only suggest that you download the app and 'hide' it somewhere, like in an app-folder that your daughter might not check very often.
Additionally, it can be 'synced' across devices so that you could change some settings on your phone and they would apply to your children's devices, but this has the caveat that (I think) you would have have to have the same restrictions applied on your phone as your children's (depending on your phone/app usage, this could be a bit annoying). Otherwise, unfortunately I don't think ScreenZen has the same parental capabilities that ScreenTime does.
That being said, it is FAR less buggy than ScreenTime, is free, and I find that the interventions for opening an app work a lot better than just waiting five seconds and continuing to use an app. There are a lot of settings that can be changed (add strict blocks, have a custom message appear before choosing to unlock an app, change how long an app can be unlocked for, change how many times an app can be unlocked, etc), and it really 'gamifies' limiting one's screen time, which in turn gives more motivation to quit addictive apps.

I want to add that I'm in no way affiliated with this app, I just really think it needs more recognition. The current implementation is maybe not exactly up to standard in terms of parents controlling children's screentime, but it's still a fantastic habit-breaker. Although this might not be the exact answer you were looking for, I still hope that it can help you.