Peace Psyah,
You have put across your definition of the Ahlul Bayt (as) clearly and I must thank you for that.
Just a question, for my knowledge, according to you then Aal e Muhammad will be anyone from the progeny of the Prophet, doesn't matter good or bad? am I right or wrong?
Peace Pagluu
Generally speaking progeny or Aal used in common speech refers to any offspring good or bad. However, in the case of Durood, it takes the meaning of only those from the progency who are praiseworthy.