I'm so sorry your daughter's having problems booking her test!
In my 40s, I decided to learn because of the pandemic. My examiner told me to book and I arrived at the test centre in February 2022. I wasn't ready, but when I looked at rebooking a test further ahead, it was months away. So I took a chance a turned up. I got to the top of the road from the test centre and... Failed. Back then, because of covid, you didn't do the whole length of the test, which is handy practice. They booted you out as fast as they could, so my test lasted 5 minutes.
My instructor told me to rebook, and the next test wasn't until June. I was absolutely terrified on the day because if I messed up again, it meant more waiting. And more money on driving lessons. The pressure was just appalling. The nerves were so bad that my legs were shaking (I nearly fell over walking from the car to the test centre) and I was braking too heavily. And yet - miraculously - I passed.
I'm really stunned that the DVSA haven't sorted the problems out. I remember back in 2022 that they were pleading with retired examiners to come back! I'm amazed at how low their wages are, too.
It makes the process far more stressful for learners and no doubt people are failing and having to restest because of the pressure. And bearing in mind that instructors train you on the roads near your test centre, taking a test at a centre miles away, on roads you don't know, would make the test harder.