are you planning on walking in any of the queues? if so, when you go to get your GAC, tell them that your medical condition prevents you from climbing stairs. Even if you can walk up or down stairs, in some lines you have to wait while standing on the stairs. When I was still walking I found this more difficult than simply climbing up and down. I think there might be a stamp to help you with this.
It sounds like both you and your child have issues that require the use of the GAC. If your needs are different, or if you're going to split up for any reason, you can get separate Guest Assistance Cards.
My suggestion though is to keep the wheelchair with you in queues as much as possible, as this is both the easiest place to push a chair (usually) because the ground is generally smooth and flat, and because you never know when the ride is going to break down or when the posted wait time is incorrect and you get stuck in the line for longer than planned.
My family has parked at the Contemporary and the Polynesian, ate at a restaurant (the guards at the gate of both resorts we'll ask what your purpose is at the hotel. They are stricter at these two resorts especially because the parking lots were full of people staying off-site who were trying not to have to pay for parking. Once my family was finished at the restaurant or store, we would sometimes go on to Magic Kingdom from there. in my experience, it would take no longer, or potentially much longer, get to your car in the hotel parking as in the standard Magic Kingdom parking lot.
I am not sure when your last visit was, nor do I know when it was created, but in addition to the regular accessible parking spaces with the blue signs and blue paint, there is now "overflow" medical parking. The result is that there is much more room near the front of the parking area for families like yours. This area does not require the use of a tram.
Can someone who has gone to Disney World recently confirm the medical overflow parking in the MK parking lot?
Also, can someone confirm that the boats between the resorts in the park can handle wheelchairs? I know that some boats are more than large enough, but some are smaller, cannot ever handle scooters, and I am not sure if they would accept even a folded wheelchair. Plus you have to climb down into it. Hopefully someone here has an answer to that question.
Have a wonderful trip!