I am not a lawyer and all I know about visitation orders is what I've read about it:
(1) typically if the parents work out a mutually-agreed visitation schedule and present it to the court, it will be included in the court order as-is unless the judge thinks it's grossly unfair.
(2) if the parents don't agree and the judge has to decide, generally the bigger the distance between the parents' homes the more the visitation schedule will skew towards fewer but longer visits.
(3) if a great distance exists because the noncustodial parent moved, the noncustodial parent will normally be expected to bear all or most of the transportation burden created by the distance (i.e. may well be expected to pick the children up and drop them off at their home or school).
my oldest is severely autistic and isn't going to be able to handle extended trips to stay with him
I don't know much about how courts handle special-needs children, but suspect that you will have to get his doctors to testify in support of your contention here, to have it taken seriously.
Moving would mean living in my sister's basement until I can get hired as a teacher, losing their health insurance, starting over with finding school, therapy (when I can secure insurance), child care, etc.
Seriously? I did a little googling, and obviously I can't research every school district's residency requirements, but I read that the MI state government passed a law forbidding cities from having residency requirements - ? Even if/when there is such a requirement, new employees typically have a grace period (I saw 6 months mentioned a couple of times) before they have to move there.
I would not recommend moving without a job, especially if Dad's ability and/or willingness to financially support the kids is unreliable. But a long-distance job search while still employed should be possible, if inconvenient.
I think your youngest two are young enough to handle moving pretty well. Most 11-year-olds can handle it decently well, too (SOME trauma, sure, but not as much as with teens), but I can believe a kid with special needs would be more difficult. Is Dad willing to help (i.e. bear the brunt of the effort needed to establish a good education plan for him at his new school, and whatever else might be needed)?
If you hate it in AR, then you might want to take another look at moving and not dismiss the whole concept so quickly. Though the way you describe your life there sort of seems to contradict your assertion that you hate it. Only you know for sure, of course, and it's not my business.