This accident was caused by human error. The question is , whose error ? It is seems obvious that the error must be shared between the two parties, but in what proportions? 50/50 ? 60/40 ? To prove that your partner was less to blame than the other driver she would need at least one independent witness.
In one breath you say ' she was keeping her distance' and in the next ' it was impossible to keep a safe distance.'
In the conditions you describe , she should have allowed at least double the normal safe stopping distance for good conditions. Difficult, I know, but that is what will be argued in court. Sadly, I don't think she stands a chance, and largely due to the actions of an impatient nitwit.