How to obtain a copy of a Medicare card?

Trying to transfer my sister-in-law from present nursing home to one closer to family. She is on Medicaid and was in a nursing home close to son who has passed away. Her surviving son has DPOA and lives far away and is in bad health. He cannot find any information we need.....New nursing home REQUIRES a copy of Medicare card and apparently the nursing home she resides in now did not require a copy of her Medicare card prior to admission. We have called Medicare.gov (they will send a new Medicare card to the current address they have on file but she no long resides there); contacted nursing homes where she previously resided who have been sold and don't have the records for that period of time; gone to local Social Security office; gone to local Motor Vehicle Department, all with no luck. We now are told we will have to have a copy of her birth certificate and that cannot be obtained by a sibling. The son is agreeable to having his mother transferred but not able or willing to go to extra efforts to get the documentation we need and wants to retain DPOA. Anyone have any suggestions? We seem to run into road blocks at every turn.