I'd say first that the daughter needs a lawyer and that I do not know the law in the particular state.
That said, typically the so-called "life tenant," the father in this case, has the obligation to pay for the upkeep and taxes on the house. On the other hand, one would expect someone else living in the house, the daughter in this case, to pay rent.
The daughter taking out the mortgage and paying her father a large sum may or may not have covered rent in addition to her payment for a so-called "remainder interest" in the house.
Who owes whom in this situation is hard to say without looking at all of the numbers.
In terms of a sale of the property, the father has a right to the value of his life tenancy, based his age and the value of the property. Without more information, I can't say whether that is more or less than the $50,000 he is demanding, or whether this, too, has been covered by what the daughter has already paid her father.
In short, the outcome of this matter will be determined by the facts. It does show, however, that any transaction concerning real estate should be carried out with all of these issues discussed in advance.