Inpatient hospital wants to go to another NH when released not the prior one? Is that a big deal?

It depends upon a lot of factors. Is she private pay or Medicaid? The people who really know the answer are the discharge folks at the hospital.

Medicaid,

Then you REALLY need to talk to the discharge folks. Man NHS take Medicaid, but have a limited number of designated beds. Will she be there as a rehab patient initially? In that case, Medicare would pay the first 20 days in full, I believe.

Ther may not be much choice. When someone is Medicaid they usually have to take the first available bed. It is unfortunate but there really is no choice. Look on the bright side this one may be better than the last one.

Medicaid doesn't do bed holds, so the bed she had has probably been assigned to someone else if she was gone a long time.