Always go with your daughter's insurer. From personal experience with a no fault claim also the other party like you with Admiral, found LV very good. Repairers give a lifetime guarantee, will ensure the standard of repair, and if problems it can easily be returned for rectification, not that I had any. If not her fault LV will automatically provide a courtesy car for the duration of the repair to at least the same standard of her current car. They also take care of any hassle (found LV very good with this) and pass on costs without your involvement. Admiral will try to keep costs down as they are paying!!