Does a patient need to be in a nursing rehab center for 2 months following a routine hip replacement surgery?

OK, so, not routine...so sorry!!

Her surgery was done in a hospital and after three days she was then moved to nursing rehab center,Where she's beenm for three weeks, Also she fell and fractured the hip

Depends on what are called "co-morbidities" - usually a hip replacement is inpatient a couple days then home rehab, but if other things are wrong medically and they can't manage it all, there may be reasons for subacute rehab instead. But no, probably not "hospice" - its hard to see why they would do a hip replacement for a hospice patient.

One other thought - was this an elective hip joint replacement for arthritis, or surgery to repair a fracture? The latter more commonly needs rehab beyond waht can be managed at home.

People are not put in hospice for hip replacement surgery. I suspect you don't have all the facts.