When your dad bought your nans property, the solicitor acting for him should have had a will made for your nan, the property should have been put in trust, even though your dad has the mortgage, it was still where your nan lived.
Since your nan is now unfortunately unwell, and with dementia she is not able to sign anything. Your father must get a solicitor to act for him to protect his investment.
There really should have ben legal representation from the start as he was buying a council property.
His sister does not have any right to 1/2 the property, she has not paid towards the mortgage.