You mentioned how she was afraid of the little cars in the mall that were moving. Remember, at Disney she will be on the rides with you--not placed in the seat alone. If I were you, I would hold her in line--don't even draw attention to the vehicle that she is going to be getting into with you and then just step in nonchalantly, seat her next to you and just keep talking like it's all the most natural thing in the world. Never ask, " Do you want to go on this ride? Oh, look--we're going to ride that." You just do it without drawing attention to any of it. Get the older kids in on the "game".
I would skip all character meals and photo ops with characters--until maybe your last few minutes in the park on your last day. Here is the problem--if you make a child do something (hug a character) early in your trip and they end up being afraid--they will freak out all week long because they have been traumatized. If you are going to "traumatize" her--do it when it will impact the trip the least--at the very end. Who knows, by then she might be comfortable enough at WDW to go for it!
This same strategy should be applied the the scarier rides--later in the trip--not early on. Otherwise she will freak out all week long. When in doubt, do a baby swap!!! You need to build trust with her all week. If she learns to trust you, she won't be on alert that you might spring something scary on her at any moment causing her to over react to everything. Ease her into the trip--play in the sand on a resort beach, eat a Mickey bar, ride Dumbo with her.
I had two children ( of my six) who were deathly afraid of fireworks. Might I suggest that you not be very close to loud fireworks with a child as sensitive as what you described. Perhaps view Wishes from the Poly Beach. Maybe view Illuminations from the CBR beach or the Boardwalk.
I had two sensitive children like the one you are describing. No way would I leave them home. But that is just me. YMMV. Different personalities can tolerate different things.
I agree with absolutely everything said in what I quoted! She isn't going to be put somewhere away from you; she will be WITH you. It's OK for her to be so attached, and even OK for her to be fearful right now. Just let her know and see and feel that you're there for her, and there with her, and it'll be OK.
She's attached to her close family and friends but anyone else scares her. She is afraid of mostly everything. I couldnt even get her in one of those little cars that rocks back and forth at the mall (it wasnt even moving) I took her on the Carousel in the mall and she freaked! & The toddler rides at Chuck e cheese, you can forget it. ........what am i gonna do?
Grandma has offered from the start to keep her while we go.
Don't take her on the carousel, and for everything else you'll be with her.
Took DS to
Disneyland at 17 months then just about a year later. Both trips he spent quite a bit of time being worn...first trip I had a mei tai, and he spent most of his day (they were one day trips to DL, though we also went to SeaWorld and the San Diego Zoo) on my front, facing me, in his mesh-bodied mei tai. He could see faces (instead of rear ends as they do in strollers), he could put his face into my chest if he got overwhelmed or worried, concerned, peeved, tired, etc. He could see where we had been over my shoulder, which is a wider view (for anyone who likes riding trains sitting "backwards" you know what I mean, it's just a better view of the outside that way) and nothing was just right there in his face.
Second trip he was on my back in the Ergo for much of the day and at SeaWorld too. Again, he could see at my eye level (well, almost), he had me right there, he could rest his head on my back...I was protecting him at all moments when he needed to be protected. He did walk around much more on that trip, and was in the rental stroller once (we didn't even own a stroller until *after* that trip) for about 5 minutes...just as he got used to it we got to it's a small world, and then he didn't want to get back into it after riding, LOL.
You can really protect littles while showing them fun things at the same time. I wouldn't leave her with grandma... Even if she doesn't want to interact with anyone but you guys, on the *next* trip she'll have the pictures from her first trip to have looked at, she'll have the feeling of you guys with her during that trip inside her "lizard brain" (what I call the part of the brain that is instinct and un"remembered" memory), and she'll probably be really psyched to see it all as a bigger kid!
Have FUN!
We have one "issue" we are worried about.....our 20 month old. She's attached to her close family and friends but anyone else scares her. She is afraid of mostly everything. I couldnt even get her in one of those little cars that rocks back and forth at the mall (it wasnt even moving) I took her on the Carousel in the mall and she freaked! & The toddler rides at Chuck e cheese, you can forget it. ........what am i gonna do? 
