Mom feels trapped in the nursing home and wants to come home, but once she is home, she feel trapped again!

I going to take a stab at this. What I think your mother is looking for is the past and her youth and her health. And that is gone. And she isn't going to find it "out there." You didn't mention how old she is or her state of health or the rest of her state of mind. I would recommend you talking to her Dr. about your mothers unhappiness and what I perceive as chronic anxiety or maybe depression. These things are very common in the elderly and can be treated with LOW dose medication. I don't like anti-depressants or anti-anxiety drugs, but there is a time and a place for these and sometimes a short term treatment can really help an elderly person and improve their quality of life.