You don't have to tell details and if your therapist expects them, I'd ask her why and have a conversation on that first.
There are a couple issues here, with this idea of spilling it all. First, it helps to talk and tell what happened because it decreases the shame and burden of keeping it a secret. So I think that's the main reason to tell what happened, whether generally or in more detail. But the question I have is does that cure the trauma? Not really. Healing might come from some amount of telling (no details necessary) in order to have your experience understood and validated, but also to be able to feel safe through all of it, maybe scared but not re-traumatized.
But the bigger issue in healing is how we work with most of our symptoms (and for many of us with childhood trauma, our symptoms are not dependent on even having clear detailed or picture-like memories...narrative type memories are often very lacking): likely any of us with PTSD or CPTSD are dealing with a lot of nervous system dysregulation that isn't cured by telling details. If not handled well, those details just spin us into deeper dysregulation. So ideally we work with the symptoms and taking care of our selves: self care, grounding, staying present (vs dissociating) managing the body responses and stress while sharing what we can, and also finding other outlets for all the trauma energy (just talking doesn't cut it for me personally).
I'm working with a body psychotherapist who primarily uses Somatic Experiencing along with other methods to meet me where I'm at. In SE, it is made pretty clear that the details of our stories are not crucial to our healing. I am not sure where that idea started, but I assume it's rooted in the belief that sharing the whole story will relieve us of shame, which is important. If that feels true for anyone personally, hopefully they are working with a therapist who can help them structure therapy in a way that allows them to share details only if they first feel safe and have done a lot of recovery work (grounding, regulation, self care, safe therapeutic relationship) aside from this idea of details.
If anything details should come quite late into therapy. So much potential for losing ground if the belief is you must start out by sharing your whole story. I go mute, dissociate, and self destruct if too triggered. Not helpful and healing or even connection to my therapist just stops. That all had to be worked around slowly in tiny pieces and waves. The idea in SE is that this trauma "charge" is let down slowly and carefully. This makes a lot of sense because I have A LOT more nervous system "charge" than I have details of all trauma in my memory. Some of my details are very fuzzy at best.
I'm glad your therapist was willing to leave it alone when you froze up. Sounds like she gets it.
We spend a lot of my time working on body work and learning tools for staying present, which makes sense to me given my past.
That sounds very good, and likely more empowering to you right now.