Anne,
To start off - thank you for providing all the appropriate and relevant information.
All other apps do not seem to have any problem selecting Tray 2? The A3 page size? Test prints are working just fine, etc.?
Is there another machine you can test? I really don't want to start to bugger up your machine - if at all possible.
In a former life I used to be a building/facilities engineer. The first rule of building maintenance is to not fix that which is not broken (don't break what's working by 'fixing' it) - so long as the printer driver is fully operational let's not monkey with it.
If you have a test machine.... if not, you will have to guinea pig on your own box...
The first thing I would do is Uninstall Reader X, reinstall Reader 9 (incl. all the current patches) and makes sure that it still works. Yes, sometimes we need to move backwards to move forwards.
Next, I would uninstall Reader 9 and try Reader XI (eleven). Is the behavior the same as 9 or 10?
If it's the same as 9 - problem solved.
If it's the same as 10 - submit a bug/enhancement request - https://www.adobe.com/cfusion/mmform/...
Between versions 9, 10, and 11, Adobe did make some changes to the printer dialog boxes in both Reader and Acrobat product lines. Sometimes they get the changes right. Sometimes they break things.
I hope this helps.
Thanks
Doug