That’s a difficult and not unusual situation. Legally, your mother cannot be forced to move unless your wife or another family member is appointed as her guardian or conservator (different states use different terms). Then she would be able to make these types of decisions for her mother. However, sometimes it’s possible to get people to move in other ways.
For instance, you might be able to get her to try it out for a week or weekend to see how she likes it. Often, unfortunately, the placement occurs as the result of a hospitalization. Things deteriorate to such a point that the senior needs hospital care and then gets discharged to the facility.
A geriatric care worker may have ideas for other good strategies.
Harry S. Margolis practices elder law, estate, and special needs planning in Boston and Wellesley, Massachusetts. He is the founder of ElderLawAnswers.com and answers consumer questions about estate planning issues here and at AskHarry.info.