The park has the majority of the staff; they run the Pirate show and Theatre show as well as Scarefest when it is on. The Hotel has 2 technicians; the conference centre has 1 technician. The rest are generally on or around the park. For example Pink did a gig at Towers in the summer of 2010 that as far as I am aware, was done by Pink's designers etc. The Ents team will just assist, as from what I heard when I was there, it is external.
For the shows Alton Towers host, like the hotel shows, pirate show, theatre show and Scarefest - their own equipment is used. They have a wide variety. The hotel show uses Avo install dimmers and a pearl tiger with a load of white Mac 250 entours. Whilst the Theatre uses Arri install dimmers and a Jands Vista T2 outputting to 20 or more Coemar 250 prospots, which is triggered via a Medialon V4 system. Sound in the theatre is an LS9 running a mid size PA. The laser show was run on 2 of the old Compulite desks (Micron 4D) that they still have in storage. As far as I am aware they ran the Ice show back when it was running too.