We completed her trip and it all worked out well! Here's an update of how it went:
We did one day at each of the four theme parks. She was fine walking to the tram, entrance, ferry, etc. and we reserved a wheelchair inside each park. A couple times we used a courtesy wheelchair back to the parking lot and/or tram after returning the chair at the end of the day. It was all very efficient, more so than had we tried to wrestle an off-site wheelchair in the car, particularly since she didn't need one for any of our non-WDW days. So it would have been an inconvenience to be hauling one around.
She is mobile enough that we parked the wheelchair outside places like The Land and The Seas to go in and ride Soarin', Living With the Land, Nemo, etc. She stayed in the chair for some shows (Birds of Flight, Nemo and Lion King at AK; The Little Mermaid, Frozen and Fantasmic at HS) but transferred at Indiana Jones and Beauty & the Beast. We wheeled her in the chair through the queues for Pirates, Na'vi, AK Safari and she transferred to the ride vehicles. We parked outside Mexico to go on Gran Fiesta.
They (MIL and sister-in-law who traveled with her) decided they did not want to do the Candlelight Processional because the dining option menu I was able to get wasn't of interest, and we only had a reservation for the 8:15 pm show which they thought was too late due to jet lag. For the same reason, they were not interested in seeing fireworks at either MK or Epcot. We were lucky to be at HS on the evening that Fantasmic was at 6:30, so did that.
She even managed to navigate the walk onto the Skyliner to get from the HS parking lot over to Epcot so we could enter at the International Gateway and get the wheelchair there for our Epcot day.
Not all the WDW wheelchairs are in the best condition. We had to return two (one at HS, one at Epcot) and swap for different ones because they either didn't roll straight (like when you get a bad shopping cart at the grocery store) or one of them kept collapsing and folding in on itself (she is a small woman, so it wasn't weight).
We also made it to Wilderness Lodge for a visit, intending to eat at Geyer Point (but there was a 1 1/2 hour wait). We took the boat over to Fort Wilderness and she managed the walk from the boat dock to the stables and back (my SIL wanted to see the horses). And on the way to the airport, we spent a couple of hours at Disney Springs where she managed a walk through the shops and Starbucks and back to the surface parking behind Cirque.
All in all, it went well. Thanks to all who posted with tips and advice, it was super helpful in planning and setting expectations. Hopefully this thread will be helpful to someone else in future.