Would the house be considered 50% mom's and 50% split between us three girls if my father died without a will in 1973?

In Texas there are a couple of questions that need to be asked. Was the house community or separate property? Next are there children outside this marriage, such as a previous marriage? Since you say it is your mother and father, I will answer as if your sisters are also the product of this marriage. If the house is community property, it belongs to your mother. If the house was your father's separate property, it belongs to you children. She however, has the right to live in it all of her life. Whether her stay in the nursing home is sufficient to remove that right, is a whole different question.