I will say this - the wheelchair entrance does NOT always mean a quieter place, shorter line, easier place to wait, less confusing, or better in any way.
As an example, I went to DL today and I have both a person manual wheelchair and a GAC. Obviously I always go in the wheelchair line, which is often the mainstream line.
I took a photo of the accessible line at Jungle Cruise (which is is considered a "C" ticket ride or so) (also many people with certain GAC stamps end up here). It actually took me 3 photos to get the whole line. And this is pretty normal for a moderate season Saturday. The line was just as long, anhgd in my opinion, busier than the standard line. I will post the photos later to show what the "accessible/GAC" line is. If I could have, I would have gone in the regular line, but it has stairs.
Something to keep in mind is that in DL, the wheelchair entrance is usually in full sunlight. And at the exit, so you are fighting people coming out to get in.
Honestly my sensory issues are helped more by my wheelchair providing personal space than my GAC.
Depending on the age of your child, I think using a stroller as a wheelchair (you get a GAC for that) would be your best bet. That way you use the wheelchair accessible line, but it would give your child personal space to avoid touching, etc. Also, you can have a shade, which may be very important.
On a busy day like you are going, I would expect, no matter what GAC you have, for the wheelchair accessible lines to be as long or longer than the standard line.
GACs are not intended to shorten the wait time, and on a busy day like that, they really won't.
Being able to keep the stroller with you may be your best bet. And it is treated like a wheelchair in this case, so you use accessible lines and get access to wheelchair viewing areas and wheelchair areas in theatres.