I would suggest calling the ADA technical assistance center in your area for clarification. Some of the processes and protections in the ADA have shifted somewhat and they can provide you materials you can pass on to the school or union rep (not all are well versed in the ADA) and/or help know exactly where the line is now.
Are they requiring the records to be released as conditions of employment or the accommodation or asking for your consent to see if you’ll bite? It’s two kind of different things.
Your employer is in the wrong to press in, but in terms of what is worth the fight, and what is worth ignoring as the solution, might be worthwhile to sort out. If the doctor released the records, and the school used them, you would have a solid case you were violated with damages.
Right now, yes, asking for the records is wrong, but they are asking for your consent to get them and because you and the doc continue to say no, stopping the problem? that’s probably why the union rep isn’t yet fighting it. The outcome of them fighting it would be no records released and maybe the level of request would be reduced... with a big battle.
Do you have to continue to respond at all to further requests? If you have provided the documentation to continue to justify the accommodations, and communicated no to the rescuer for more, are you required to keep engaging on these requests for more? If not, I’d suggest just ignoring it. You’ve answered and it sounds like it’s been a clear response well documented.
I’d be upset too if I was in your shoes, and I encourage to you not take their bait that their lawyers are fishing out to get you to react or give in. Stay steady with your boundary. Sorry they are so adamant.