Without a right of survivorship, the distribution of the home would depend on the family facts as dictated by Texas statute if the spouse dies without a Will. In this case, you should have an attorney prepare a Will to gift the home appropriately.See question
If there are financial matters that need to be settled, you would need to be named as administrator to handle these affairs. This would mean you would file to probate without a Will. This would require a court procedure to determine of the proper heirs before the administrator is appointed to handle the estate. All the proper heirs would receive their fair share of the estate.
If all you need to do is transfer the home, then a Small Estate Affidavit would suffice. There are requirements that need to be satisfied before this procedure is allowed. All the proper heirs would receive their fair share of the estate.
You will need the assistance of an attorney to determine the best approach.See question
Because more than 4 years has the deaths of both parents, you can only probate the Wills as a "Muniment of Title" which just basically acts as a deed to transfer real estate. If there are no debts owed by the estate, you should be able to hire an attorney to handle this matter. You will need to explain to the court why the Wills were not probated within the 4 year time frame.See question