what is the definition of Ahl ul Bayt

No need to apologise brother.

The way I see it is that when Allah (swt) says something in plural it stays plural.

So when the word “Our Women” is used it can only imply Prophet (saw)’s wives and daughters.

I am not going second guess why Prophet (saw) did not take his wives along but only thing that comes to my mind is Prophet (saw)’s geerah (I think it translates as man’s jealousy concerning his wife/wives.)

brother righteous – you have conceded that wives are part of the family but the word the Ahlul Bayt is in Arabic meaning ‘people of house’ and can only mean man's family.

Brother, there is another incidence in Quran where Allah (swt) has addressed the wife of a Prophet as Ahlul Bayt [people of the house]

Qalat ya waylata aalidu waana AAajoozun wahatha baAAlee shaykhan inna hatha lashayon AAajeebun

11:72 She said: "Alas for me! shall I bear a child, seeing I am an old woman, and my husband here is an old man? That would indeed be a wonderful thing!"

Qaloo ataAAjabeena min amri Allahi rahmatu Allahi wabarakatuhu AAalaykum ahla albayti innahu hameedun majeedun

11:73 They said: "Dost thou wonder at Allah's decree? The grace of Allah and His blessings on you, o ye people of the house! for He is indeed worthy of all praise, full of all glory!"

And there are authentic hadith where the Prophet (saw) addresses his wives as ahlul bayti.