In episode 3, there are actually three Kyle McLachlan characters. Dale Cooper, FBI agent wearing his familiar black suit, is trapped in the other-worldly red room. #2 is the hard boiled criminal character, also referred to as Cooper, and involved in FBI work. Number three is a kind of duncey character named Dougie who lives in Las Vegas and sees prostitutes, but we've only seen him just lately, and briefly.
The entire episode (1 hour) is dedicated to showing the movement of characters in and out of their dimensions, and how they swap bodies. We know from other films that Lynch loves to move the camera into other worlds. The camera will follow the sound coming from a telephone earpiece, and go right through the holes in into the electronics. Or the camera will travel through walls to show the spaces inbetween rooms, with dust, drywall matter, and rodents.
So here Lynch seems to have put quite a lot of thought into the experience of being in a strange dimension. The black-suited Cooper leaves the red room and enters into a creepy limbo. There is a woman with missing eyes who can't speak, in a room with a strange steampunk apparatus in a wall panel, and a metal door somebody is heavily pounding on from the outside. They climb up a ladder, open a hatch and climb out onto a platform suspended in outer space, very much like Le Petit Prince standing on one of those little planets, but more terrifying. The woman falls of the platform and presumably falls for eternity. Eventually Cooper climbs back down, and a woman in red by a fireplace advises that he must go NOW. Cooper ends up passing through the steampunk apparatus, painfully...and leaving behind his shoes.
The other Cooper, and Dougie, back on earth, experience extreme vomiting. Dougie shrinks to nothing and black-suited Cooper comes out of a wall socket in the form of a black gas, eventually appearing in solid form laying on the floor. His faculties haven't recovered, and he is a Rain Man-style imbecile. He ends up in a casino, and starting with a $5 bill, wins enormous payouts from every slot machine he tries. He eventually gets picked up by the authorities, and he's reported to FBI headquarters where Gordon Cole, the hard-of-hearing senior FBI guy played by David Lynch himself, celebrates the news of Cooper's final return.
The tough-guy Cooper ends up in a car wreck, and we don't see what's become of him physically.