The shop manual for this van says that the way you have to do this is to drill out the four bolts that hold the handle into the door frame. Lisa spent a while trying to figure out a better way. The way the door is put together makes is so that if the door was already open, it would be relatively easy to get at the handle. You have to remove the plastic inside door panels from the door frame, but the only way to do that is to have the door open already, and of course the door was stuck closed.
The door is held closed by two latches, one at the top and one at the bottom. The door handle, when it works, actuates a couple of lever arms that open the latches, which engage to a bracket attached to the vehicle body. Lisa did manage to get the upper bracket off by pulling away the interior body work just barely enough to get a wrench on the bolts. She did the same on one of the two bolts on the bottom. She then asked for my help as she tried to get a screwdriver to disengage the lower latch while I lifted and pulled on the door.
We tried lots of different ways of pulling and twisting on the door, but none of them worked. After at least an hour of this, Lisa decided to try again with the wrench on the bolt. Because her fingers are small enough to fit into a space where you really aren't expected to be able to reach, she was able to just barely get the box wrench onto the last bolt. She could, with much effort, get it to turn about one-eighth of a turn, after which she had to pull it out and reach in again. As the bolt came out, it got harder to actually reach it with the wrench, and as you can expect, it took a long time to actually get it loose.
With considerable effort, Lisa got the final bolt out, and the door swung open. After that, the repair went pretty swiftly. She quickly removed the screws holding the plastic panels in place and popped them loose. I set them aside while she reached inside the rear door and undid the four bolts (the ones the manual says you have to drill out to remove) from the inside. The broken latch came out easily.
Lisa took the new latch that I bought from GM a few weeks back and fitted the lever arms to it. She tested the latch a few times with the door open and it seemed to work. Now came the scary parts, since they could end up with the door stuck shut again. She re-attached the bracket on the top of the rear frame and closed the door. The latch easily opened. She then re-attached the lower bracket (which took about a minute rather than the hour it had taken to remove it) and we crossed our fingers and closed the door. She pulled on the handle. Success!
We tested the latch several times, and it released easily. It shows no signs of the difficulty it was having before it broke completely, probably because Lisa got the levers back where they belong on the new handle. (We postulate that the levers had slipped, and the extra stress I'd been having to put on the handle to get the door open was what broke it in the first place.) She opened the door, I took the opportunity to dust out the inside (it's unlikely it had ever had the panels off since it was built in 1988), and she popped everything back into position and screwed the panels back into place.
The rear doors now work properly again, so I can move things that are wider than one door again. I expect a body shop would have charged at least $250 in labor and maybe more, and they might have tried to use a lower-quality Chinese clone of the part. While I paid more for the genuine GM part, I was glad of it and glad they still stock the part.
In light of the labor savings, I didn't begrudge buying lunch from the burrito stand a couple of blocks from here on Main Street or taking Lisa out to dinner last night at the China King Buffet down the road one bit.