It's difficult and unpleasant to acknowledge what happened. By doing so they would have to acknowledge and deal with what happened in the past (that caused DID in the first place). Part of therapy is to take them on this road. They're able to cope with reality because they're able to compartmentalize their history. Hearing about it, while necessary, weakens the coping mechanism that helped them survive. So you can imagine why they wouldn't want to hear about it.
And on a far more simple level, disassociating and returning from it is utterly terrifying, and worse still one might know that their loved ones will have also had a very difficult experience
I've seen that "exposure" therapy is often used in the treatment of OCD, another form of anxiety disorder. Patients with OCD often have an anxiety about something and use their quirks and rituals to avoid/ignore the anxiety. To help them cure their rituals, they must actively try to experience the often very extreme anxiety that some situation puts them in. Is the treatment similar in cases of DID?
No, that would be too much for a DID patient and could lead to further splitting (creation of new parts). First step is to teach them to stay grounded, to stay present and not take the easy path and dissociate (i.e. go away). When struggling to stay present someone with DID may exhibit OCD patterns -- scratching, grabbing, fiddling with fingers etc. -- all without realizing. However, when this happens there's usually some level of co-consciousness with a part that is suffering or has OCD. So in this case the OCD behavior would "belong" to that part while some other part is "out" (they'd actually both be "out" at the same time). It's a very complex disorder.