I know how frustrating the whole process is. Just know that the entities involved don't always tell the truth when it comes to their obligations.
Even though the school district isn't in your town, they are still obligated to provide services for your DD if she's eligible (they're receiving school tax dollars as well as state and federal funding for the students in your town).
See they don't recieve any money for the kids in our town. We have our own tax base and because we don't have a public school we don't pay state taxes like others do. The arrangement our town has is sort of a private arrangement that was made many many years ago. It has been let stand because of how long it has been in place.
When it comes to a 504 and religious schools, if they receive even $1 in federal funds, even indirectly, then they have to comply with the 504 law
After battling with our school for 6months over the diabetes issue I'm certain they don't recieve and federal funding. When it comes to the ADA, it applies to all institutions/businesses that serve the public in any way. Here's a link that might exlplain that further.
http://library.findlaw.com/2000/Mar/1/132912.html
However, even with all the laws behind you, many institutions/school districts won't do what they're supposed to until lawyers become involved. They're basicly assuming that you'll blink first and they won't have to spend the money on the services/accomodations.