bran--first, book wheelchair assistance through AA. Easy to do online. There is no cost for that. That will allow you to bypass the lines in immigration and baggage. Also they will be responsible for transporting her by wheelchair within both airports, if they make you check the wheelchair. As far as the collapsible wheelchair, my suggestion is that you contact AA by phone and ask them whether you can take it onboard or not. My inclination is that they PROBABLY will require you to at least gate check it, if not baggage check it from Miami, It is worth a call ahead of time to see what their policy is.
As far as stairs, it depends on the plane. SOME planes get a RAMP to disembark, but not all. Some planes have stairs at front and back. If there is a ramp, it will be at the front of the plane only, with stairs in the back. Since you are in first, if there is a ramp, you will have it. If you call AA ahead of time, they should be able to tell you if you can carry the wheelchair onboard and whether there will be a ramp when you arrive. Depending on your wife's abilities, she may be able to use the ramp to disembark, even without the wheelchair.
We leave a few days before you arrive, as otherwise I would love to meet up with you on island.
What did you decide to do on lodging?