" I am being told that this is a nominee trust."

Has anyone provided a copy of the trust?  I would not rely on blind faith to figure out what really happened.  Is this in New York?  Small-town lawyers there enjoy doing things with life estates and remainder interests, that you don't find in other parts of the country. 

Daughter, or her trust, always had title to a remainder interest. When mother died, the trust acquired the whole thing.  If mother continued to live there, it's probably covered by Section 2036, so would be included in her estate, so gets stepped-up basis.  But it might depend on what's in daughter's trust.