The Original Ending
Below you'll find the original scripted ending of "Poltergeist III." Although Mr. Sherman said he'd donated his only copy of the shooting script to the Margaret Herrick Library in LA, I was able to purchase a copy of a slightly earlier draft from Heather O'Rourke's sister, Tammy. Luckily it came with storyboards of the original ending! I've posted both below.
note: The script excerpt is copyright1987 by Gary Sherman and Brian Taggert/MGM. The storyboards are copyright1987 by Brick Mason/MGM, and the publicity stills are copyright1987 by Dean Williams/MGM.
REVISED: 3/18/87
CONTINUED:
ANGLE-PAT AND CAROL ANNE-Pat recoils in horror, wildly swinging the necklace at the evil presence in front of her. Carol Anne steps back, disappearing into the fog. Pat unlatches her safety belt and plunges from the washing rig through the broken window and into the screaming maelstrom. 
INT. CAROL ANNE'S BEDROOM-GARDNER APARTMENT-NIGHT
Pat tumbles to the floor in a room which has become a world of pure, freezing rage. Shielding her eyes from the icy light and howling wind she staggers forward, searching and screaming.
(above, a storyboard showing the placement of the frozen bodies in Carol Anne's room)
PATRICIA
Bruce! Bruce!
She is startled as a violent gust suddenly forces her to lose balance and she collides with a solid object. She falls and turns to it. 
HER POV-She is eye-level with the top of Carol Anne's bed. A few inches away, Carol Anne's Speak 'n Spell, frosted with ice suddenly comes to life. Its sound eerily cuts through the din.
SPEAK 'N SPELL
B-R-U-C-E. Bruce. Can you spell Trish?
CLOSE ON PAT-As she scrambles back away from the bed. She falls again over another object on the floor. It is Carol Anne's body, frozen in the throws of death and pinned to the floor by a solid sheet of ice. Terrified, Pat screams and rolls away. She is immediately confronted by another ice statue. This one contains the bodies of Donna and Scott, twisted in death beneath the ice. Pat recoils and stumbles onto a third ice statue. It holds the grotesquely frozen body of Bruce. She screams in agony and horror. 
PATRICIA
Bruce! Oh my god...Bruce!
Pat throws herself at the frozen form, desperately beating and clawing at it with her hands. Her eyes wild with emotion, she suddenly focuses on something.
HER POV-She sees Kane looking down at her through the ice and fog.
ANGLE-PAT-As she rises and hurls herself at Kane. She SLAMS into the mirror. With a passionate fury, her hands madly tear away at the ice and frost on the surface.
PATRICIA
You can't take them! Tangina said you can't. I love them! I love them!
She suddenly stops. She spins around, realizing that Kane is not behind the mirror, but behind her in the room!
HER POV-KANE is moving toward her. His face is the pure essence of evil. The foul decomposing champion in this war between life and death. He grins behind his cold breath.
ANGLE-PAT-As she slides along the mirror, just out of his grasp. She is crying.
PATRICIA
NO!
Suddenly, Pat's mirror image spins around, it's face a death mask, it grabs her viciously. It reaches for the necklace. Kane laughs as Pat screams. She hits out at her evil image. It releases its grip.
(above, notice the red object on the bed in the background? This is likely Carol Anne's "frozen body")
ANGLE-PAT and her mirror image fall back.
ANGLE-PAT-She has fallen over the frozen body of Tangina, pinned like the others by a sheet of ice to the floor. Tangina's eyes move beneath the ice, panning from Pat upwards to Kane.
(above is a pic of a model head of Zelda Rubinstein that was recently placed on Ebay. The metal piece was used to move her eyes to the right-as part of the "frozen Tangina" at the end).
ANGLE-KANE-As he approaches, reaching for the necklace, 
(above, what appears to be the "frozen Donna" at the foot of the bed, "frozen Bruce" behind her on the floor, and behind Kane to the right, "frozen Tangina" on the floor, with her hand sticking up out of the snow. For a much larger, much higher quality version of this pic, see www.poltergeistIII.com/frozenfamily.html)
ANGLE-PAT-She pulls back the necklace
CU-PAT'S HAND-Tightly clutched about the necklace. CRACK! Suddenly Tangina's hand breaks through the ice and takes the necklace from Pat. 
ANGLE-TANGINA-Rising from the frozen prison, she holds the amulet upwards toward Kane. 
ANGLE-PAT-She watches in horror.
ANGLE-TANGINA AND KANE
TANGINA
You need me, Kane! Not them! I'll guide you. I can lead you into the light.
(holding up the necklace)
I have the power.
KANE ROARS. He reaches out and touches the amulet. SUDDENLY...
CLOSE ON KANE-His face begins to crack. Fracture lines radiate across it. His face shatters and EXPLODES! with a blinding light.
CLOSE ON TANGINA-There is a slight smile on her face as the icy white light from Kane's exploding face wipes away Tangina's image.
CLOSE ON PAT-As the light obliterates her, resounding through the storm.
EXT. JOHN HANCOCK BUILDING-NIGHT
A catastrophic violent surge BLASTS! through the window sending energy swirling up through the clouds. Its dissemination creating prismatic beams which shoot up into the sky, dissipating, absorbed into the vast dark expanse.
INT. CAROL ANNE'S ROOM-GARDNER APARTMENT-NIGHT
The storm is quickly dissipating-Visibility returns. THE CAMERA MOVES IN ON BRUCE, PATRICIA, DONNA, CAROL ANNE, AND SCOTT. Their arms intertwined around each other. The five of them together in a family embrace sharing tears of joy and relief. Bruce has lifted Carol Anne. Pat stretches up and kisses her lovingly on the cheek. They are all facing away from the mirror except for Carol Anne who is facing it over Bruce's shoulder. Her eyes focus on the mirror.
HER POV-In the mirror is the reflection of the whole group. Amid them stands Tangina. She smiles into CAMERA and waves a gentle "goodbye" to Carol Anne with her fingers.
ANGLE-CAROL ANNE-As she returns the gesture, a solitary tear wells up in one eye and gently rolls down her cheek.
ANGLE-OVER CAROL ANNE-and into the mirror. Tangina appears to walk around the group and in front of them. Carol Anne turns her head into the camera.
HER POV-There is no one in front of them, just the silence of the room and the remains of the broken window looking out to the skyline.
ANGLE-THE FAMILY AND SCOTT-Tangina is no longer in the mirror behind them. All that remains is a family together and safe. THE CAMERA BACKS out of the room and passes through the unbroken window. It PANS across the face of the building, finally settling on the morning sun rising over the shimmering waters of Lake Michigan.
THE END
SHOOTING SCHEDULE EXCERPTS (of course this schedule may have changed; but it does seem the very end was supposed to be shot first, then on three days later the actual fight between Tagina, Kane, and Pat)
6/16/87
Tuesday
1.Carol Anne sees Tangina in mirror only, they wave goodbye
2. Final shot. Pull away from family.
3. Storm dissipates to find the family happy and full of love.
(All cast and mime doubles involved)
6/19/87
1. Pat struggles blindly thru room and runs into her frozen family.
2. Kane goes after Pat for the necklace.
3. Tangina breaks out of ice to save the day and is obliterated by Kane's facial explosion.
4. Kane's face explodes.
5. Energy surge exits hole in window.