Hi Guest,
It is true that the lenders will want the co-signer to be added on the property deed. So, there is nothing wrong if the lender had wanted the same in your mother's case. Your mother won't be able to remove the son's name from the property. After she refinances the mortgage solely in her name, she will have to ask her son to sign a quitclaim deed and transfer the property to her. This will make her the sole owner of the property.
Why didn't see do a Reverse Mortgage instead? It sounds like it would have been a better solution.