Take the cover off the passenger rear door.
Get a mirror, camera, or bore scope and watch how the latch parts should work.
You should be able to move the latch mechanism with a big flat blade or small pry bar.
It may be possible to move the child latch lever from inside the door.

Or talk to a body shop. at worst they should be able to cut a flap to allow for easy access (and un noticeable repair) and some lubricant and hammering should get it open if it is actually jammed.

What you are describing is usually caused by a rod being disconnected from the latch due to a plastic rod retainer breaking.

I have opened other car doors (at parts yards) by moving latch parts when the rods were missing or damaged.
Without looking I expect the Impala is no different unless you have a very rare latch problem.

 

Maybe you have same problem I had:

I just fixed my two rear doors that stopped working from the outside last weekend. I thought similar things.

But, it turned out to be the handles. The handles are metal and so is the hinge pin. But the other part of the 'hinge' is plastic. This is the whole part of the outside handle other then the part you pull up. They both cracked at the rod side.

Got a new pair from 1aauto for 27 bucks. At least on the rear doors, it's a real easy job once you know how. DRILL OUT THE RIVETS. Even if it's not the handles. You gain great access by removing the rivets from the arm rest bracket and lock module. Then undo the 3 latch bolts and everything thing swings clear. Takes less than an hour per door start to finish.

On the rear doors, you can easily get to handle back nut with a wobble extension inserted through the latch hole once it's out of the way. The front nut is just a socket wrench as nothing blocks it after you move the lock module.

 

I have this same problem on my car now, the rear driver side door won’t open from the inside or outside . Is this the part I need to fix it ?

 

My issue was just the outside handle wouldn't open door. Part of outside handle broke inside. Yours sounds different.

 

The rear driver side door on my 96 impala will not open. The outside latch feels like it has become unattached and the inside feels like it is locked out probably from the child safety lock and will not move. Is there anyway that I can get the door open? I took off the cover around the door latch but both the unlock rod and the open rod would not open the door. You can move the unlock rod but the rod to open it will not move. It feels like Something is holding the rod from moving. There is no way to get back farther where the latch is at because you can’t open the door! Anyone have any suggestions? Does anyone know if you can somehow play with the computer to turn the child safety lock off?
Thanks, Robert.

Did you figure out what it was ?