Disney does not have any "government" discounts except for Shades of Green which is for active & retired military and DOD emlpoyee only. (and SOG is really run by DOD not Disney).
The Swan and Dolphin offer a government discount BUT it is not per diem. (it's usually around $129 per night)
All of the chain hotels around WDW (Marriott, Holiday Inn, etc.) offer government rates on most of their rooms. You can go to their websites and play around with your vacation dates and check GOVT RATE when doing a search to see your options. Some specifically ask if you are on orders others don't seem to care.
Check with your agency--this seems to be a very gray area----some agencies tell their employees they are NOT entitled to the government rate for personal travel--others tell them it is ok.