There is nothing with this DVD player that swivels. It opens like a standard laptop PC and doesn't go beyond 180 degrees. In short, what you see in the picture is the only real option for viewing configuration.
The case is a fabric case with a elastic straps. The DVD player fits into the elastic straps very firmly. You need to take it out of the case to insert a new DVD. It attaches to the seat with velcro straps, so there is way to swivel it.