Can my sister keep me from visiting my sickly Mother (80)?

Your sister may have made arrangements with a court of law to keep you from visiting your mother. And yes, they can keep you from your mother. Usually there is some objective evidence that your presence is bad for your mother. Please consider what you may have been doing to aggravate the current situation. If you can avoid those behaviors, maybe your sister will remove the restraining order. If you feel you are in the right and sister is wrong, time to get an attorney I suppose.

FRO? Restraining order? On what basis?

Can you arrange to visit your mother at times when your sister is out? In other words, can the two of you arrange to be civil to each other for the sake of your mom?