Assalam I do not want go into other details except to clarify the true definition of" Ahle Baiyth.Ahle Baiyth comprises of a family in a house usually consistent of husband,Wife and their children.The male child of the family continues to be a member of the house even after marriage with a lady who also becomes a member of that household.On the other hand if the female child after attaining the age gets married she becomes a member of her husbands house and she is no more a member of her parents house much less her husband.Likewise Hazrat Fatima would no more the member of Prophets house (Ahle Baiyt) after marriage much less Hazrat Ali.Simply because Hazrat Ali was residing with Prophet earlier does not make him Ahle Baiyth.It is very strange that the Shias do not include Azwaje Muttharath as Ahle Baiyth How come?Allah purifies Azwaje Muttharat.The Aya 37:130 refers to prophet Ilyas( Elijah). In short attributing Ahle Baiyth to Hazrat Ali Hazrat Fatima & their sons is not right. Further more Shias dont count three other daughters of Prophet.