The Special Assistance program underwent a lot of changes when Jay Rassulo took over after the Pressler Years. It is harder to get one, but if your grandmother has her own wheelchair and has a disabled card or slip they can accomidate you at City Hall. They also still rent them at the front of either Park and you can go back and forth between the Parks.
I would think the day before will be very crowded because most people will think that Thanksgiving day itself will be crowded, go the day before, or after. I have been the day after, but never the day before or the day itself. I hope some others jump aboard here and have an answer for you.
Whenever you go, I hope you all have a great time. If you haven't been in a year or so, you are going ot notice a lot of happy changes in the Park.
if your guest is in a wheelchair, there is no need for a pass at all. The attractions can now accomodate her (and your party) through the STANDARD QUEUE. If the queue is too narrow to accomodate a wheelchair, then you will be allowed to use an alternate boarding area (such as the exit). There is no longer a need to wait in the line at city hall for a GAC.
-"We can see a new horizon...built on all that we have done..and our dreams begin another thousand circles 'round the sun!"
-- Epcot: Illuminations "Reflections of Earth"
-"...Each dream that you chase, each wish you embrace can lead to a fabulous faraway place...!"
--DCA: World Of Color
It is true that you don't need a pass for the chair. But, unless things have changed completely since I was there in June, the majority of attractions at Disneyland park are NOT accessible. Your Grandma will need to use the exit to get on most of the rides. Most of the Cast Members are very accommodating . Now, if you will be visiting California Adventure - most of the attractions are wheelchair accessible.
I've been in a wheelchair the past few weeks and the only lines I've waited in that were wheelchair accessible were rides at DCA, Buzz Lightyear Astro Blasters and It's a Small World.
By the way, they try to make you walk when you go to Haunted Mansion. They ask if you can manage without your wheelchair which is ridiculous when I'm there in plaster cast, a boot over that, and crutches lol. But nonetheless they do ask so just be prepared.