I'm in ILLINOIS, I have seen people who have had to leave the nicer facilities when their insurance ran out, if the facility doesn't have any Public aid beds available, yes they have to leave. I would question what you were told. Yes, the variety and level of care at each facility is diverse and as expected, the ones that have a higher percentage of Medicaid/Public Aid residents tend to be much worse. Staffing a LTC facility isn't easy, for the most part you are asking the CNA's to do a very physical job, that is often very nasty (getting all kinds of bodily fluids all over you on a daily basis, toileting residents, doing difficult transfers, etc) and most of them are paid 10/hr. and there are never enough CNA's on the floors.
Definitely your dad needs to finalize the divorce or it could screw up her application for Medicaid.