I could not write much before because yesterday was our last day at WDW and today was travel day.
Here is some further information.
Our one and only experience with Disney with our daughter was on her Dream Factory trip last year. We had a GAC and the magic GKTW button, so it wasn't something we had to think about. We never thought we'd get to go back, but we will be in Florida for a family reunion and my husband's uncle has offered to pay for tickets for us to have another day at MK

. E will be in her wheelchair, but she also has autonomic neuropathy which causes problems with the heat/sun and a medication that requires she limit her sun exposure. We do big hats, heavy duty sunscreen, cooling vest and ice cold pedialyte through her feeding tube. We ducked into a/c when we needed too and she handled things well.
Someone who is using a wheelchair and just needs an accessible line will probably not need a GAC at all - the CM can see the wheelchair and knows where to send the guest.
A GAC is just a way of communicating to CMs what needs the person has. In your daughter’s case, she does have more needs than just the accessible line, so a GAC will be helpful to let the CMs know what her needs are. Go to Guest Relations and explain the things you mentioned here. They will give her a GAC to meet her needs - what exactly, we can’t say because Guest Relations determines that based on the needs explained by the guest.
Some attractions have an alternate place to wait that is cooler or out of the sun - whether they can offer that or not depends on what is available at that attraction and may depend on things like how busy it is (at some times, it may be faster to just go thru the regular line, so they will send you there). So, we can’t tell you exactly what will happen at a particular attraction and if you go in the morning and again to the same attraction in the afternoon, the GAC could possibly be handled in 2 different ways (both correct).
Depending on just where you are and what time, the line may not be in the sun at all. Also, depending on what she wants to ride, you should be able to plan for an outdoor attraction/wait area and then go indoors for the next thing.
We had virtually no wait time on her wish trip.
Many people on Wish trips have a special GAC that is only issued to children on Wish trips that allows them to go ahead of everyone - even other people with GACs. Those GACs are only for Wish trips, so you won’t get one like that, but they will give you one that will meet her needs.
So my question is, since she'll be in a wheelchair, should we bother with the GAC? I mean for the heat/sun issues like for the few rides that don't have shade?
As you mentioned, most rides do have shade, but heat may still be a factor (it was warmer than usual while we were in WDW - over 90 each day). June is typically in the 90s, with a lot of afternoon thunderstorms, which means high humidity. I assume that she probably does not do well in high humidity either, so that is something else to keep in mind. The thunderstorms typically happen around 3pm, rain for a fairly short time and then clean up in late afternoon or evening. So, you may want to plan for your outdoor activities earlier in the day. The sun is most intense between 10am and 2 pm, but it is usually hottest between 1pm and 5pm.
If she wants to do some of the things longer inside things, I would save some of them for the hottest parts of the day or do them as a cooling off after being on an outdoor attraction. That would include attractions like Mickey’s Philharmagic, Small World, Haunted Mansion, Hall of Presidents, Pirates, Laugh Floor, Carrousel of Progress, Tiki Room and the meet and greet for Mickey and the Princesses in the Exhibition Hall in Town Square. (Recently, they started stamping GACs with a stamp that says something like “Not valid for celebrity or character meet and greets”. You can get Fastpasses for Mickey and the Princesses though and the lines are in an air conditioned building.
First Aid is cool and quite and can refrigerate medications or feedings for you. They can also store equipment if you have some you need in the park, but not with you at all times. First Aid is located next to the Crystal Palace at the end of Main Street. Look at the maps for shortcuts to get there - it seems far away, but there are usually some shorter ways there.
First Aid also has some private rooms/cubicles where you can do a feeding in private or just lie down and rest for a while.
Dumbo was a fave and strangely was one of the few rides we had to wait for. The CM didn't seem to recognize we were there on a wish trip or something.
Dumbo has moved since you went on your daughter’s Wish trip. There will eventually be 2 Dumbo rides right next to each other in the area that used to be Toontown, just past the speedway. There is pretty good shade for the line (trees and a roof). No one is quite sure when the second Dumbo will open, but when it does, it should decrease the waits because there will be more seats.
The only other attractions open in that area are the MK train and The Barnstormer ( a short and more tame roller coaster). The rest of that area is unfinished, so if you need to duck into a cool area, the only one close by at this time is the restrooms. The next nearest place would be Cosmic Rays ( a counter service restaurant at the edge of Fantasyland and Tomorrowland.)
Because she likes Dumbo, it is very popular and that area will get hot later, I would hit it first thing in the morning.
I would also talk to both your daughters and come up with their wish lists of things to see. It is very difficult in one day to try to see everything, so you may as well make some decisions beforehand on what is most important for them.
Also, because of your younger daughter’s special needs, there may be things your other child wants to see/ do that your child with a disability is not able to do. If that is the case, you can split up so she can see those things. Someone in your party can take ALL the park tickets and get Fastpasses - then, if your older daughter wants to ride Space Mountain and your other daughter can’t go on it, Dad and 10 yr old can go TWICE - using the Fastpasses that were gotten from their park tickets and also the Fastpasses that were gotten with the park tickets of you and your other daughter. (Kind of cool thing for the other child).
ETA: oh and if you don't think the GAC will be of much more use since she's in a chair, will we have any trouble with my other daughter and dh remaining with us in the rides that have separate access lines for wheelchairs?
Most attractions don’t have separate access for wheelchairs. For guests with wheelchairs and for guests with GACs, a party is usually up to 6 total (5 plus the person with a disability). So, your group of 4 will be able to stay together whether you are using a GAC or a wheelchair.
I am not sure if your daughter is in a wheelchair for fatigue issues or because she has difficulty moving, but just wanted to mention that Dumbo does not have a wheelchair car (?elephant?), but does have one where the side of the Dumbo opens and swings back out of the way. This is helpful for someone with mobility needs, but could also be helpful if she has a lot of equipment (like feeding pump maybe) attached. Haunted Mansion also has one doom buggy with a wider opening. These are called ADA cars.
If she needs to stay in her wheelchair, or is just getting tired with transferring, Jungle Cruise has a wheelchair accessible boat. Unless you arrive just when the boat gets there and there are no other guests waiting for it, you will probably have a longer wait for that boat. If she does ride in it, there is a roof section that needs to push back out of the way so that they can use the lift. Make sure they roll the roof back or your daughter will be in the sun during the whole ride.
For each area of the park, here are some large air conditioned areas:
Main Street - the character greeting in the Exhibition Hall. Also, all the shops on each side of the street are all connected together. So, you can walk all the way down Main Street on either side of the street without going outside.
Fantasyland - Small World and Mickey’s Philharmagic are the longest attractions.
Peter Pan, Winnie the Pooh and Snow White (which will be closing soon) have outdoor lines, but the attraction is indoors. They are very short though. Caroussel and Teacups are totally outdoors. There are a few small shops, some are partly outdoors. The best place to get out of the heat is Pinocchio Village Haus.
Tomorrowland - Buzz Lightyear, Stitch’s Great Escape , Caroussel of Progress and Laugh Floor are all longer attractions. Laugh Floor has a wheelchair lane, parallel to the regular line. The wheelchair line gets you to the same place, but allows a bit more room and is not as crowded. The biggest cool place is Cosmic Rays restaurant. There is also a large gift shop at the end of Space Mountain.
New Fantasyland (old Toontown) has 2 outdoor attractions and not any good places to go in the heat at this time (except the bathroom).
Frontierland - Has one long attraction - Country Bears. That has an air-conditioned waiting area with a wheelchair area roped off to the side. It is next to the general waiting area, but less crowded. Pecos Bill (counter service restaurant) is the largest cool spot. On the end of Frontierland near Splash Mountain, there is a shop called Briar Patch which is fairly large.
Liberty Square - close to First Aid. Not a lot of large shops, but you could try Columbia Harbour House (counter service restaurant).