Check your loot rules, Trinity handles Trial keys just fine.All ok for my DH from 2.1.15 (not perfect but ok), but sometimes doesn't pick up legs (also keystone of trials - and that's a real problem, coz bot can't complete Rift) and don't open doors (when there is someone on another side).
As for opening doors, it really depends on weighting. If the thing that's behind the door has lower weight than other stuff, then trinity won't open the door until that other stuff is dealt with. If it's chests you're talking about you could try checking the new option "Give Higher Priority to Containers" in the tab "Object".