RE: Pokepowers that prevent Trainers/other Pokebodies to work?
as far as the previous format, HS-DE is concerned, there was Vileplume, which locked all Item cards on either side, and there was Gothitelle EPO, which locked Item cards on the opponent's side, but only if she was Active.
As for this current format, we have Garbodor to lock up all Abilities on both sides of the field (except for its own, Garbotoxin of course).
EDIT: Oh! And Gothitelle EPO is still in the format, too.
Stouland BDC locks up your opponent's Supporters if he's Active.