What to do if my father died 10 years ago while living with his second wife, who just died and left their house to the Salvation Army although he promised it to me?

Your father may have promised the house to you, but it appears his second wife succeeded to the house by right of survivorship and it was hers to give to whom she wanted. However, you may want to have an investigation conducted by a probate  lawyer of your father's estate to see if a probate was conducted and if he had other intentions or if he had a will that gave his share of the house to you, and his wife may have acquired his share fraudulently. Otherwise, it appears you may be out of luck.