Your dad died and the house your parent lived in the deeds was in him and a relative how can your mom add her name to them?

You need to determine how the property was titled with the other relative. If it was as joint tenants with the right of survivorship then your father's interest in the property automatically passed to the relative when he died. If the property was held as tenants in common then your father's estate must be probated and his half interest passed to his heirs at law according to the laws of intestacy in your state. Your mother should obtain a copy of the current deed and seek the advice of an attorney who could determine who holds title and if the estate must be probated.
You need to determine how the property was titled with the other relative. If it was as joint tenants with the right of survivorship then your father's interest in the property automatically passed to the relative when he died. If the property was held as tenants in common then your father's estate must be probated and his half interest passed to his heirs at law according to the laws of intestacy in your state. Your mother should obtain a copy of the current deed and seek the advice of an attorney who could determine who holds title and if the estate must be probated.