May peace be with you.
You say:
"But if your new discovery is indeed true then why would certain Jewish tribes would call Prophet Mohammad SAW a man from the Children of Ishmael or Ishmaelites as per this another article about authentic biography of Prophet Mohammad SAW?"
With respect, I would
strongly question the
sources used to derive this claim and subsequently ask the pointed question, what
unequivocal evidence is there that the Jewish tribes ever said this?
Furthermore, I would be inclined to contest the notion that there is an
'authentic' biography of the Prophet. The earliest comprehensive biography of the Prophet was written approximate
150 years after the death of the Prophet and was transmitted to us often in recensions via other students.
The authenticity of these sources is highly debatable.
Please see the article
[1] below.
The earliest, most authentic source of the Prophet's biography and wider ministry is the
Quran itself. I have shared my humble perspective in an article from the
Quran's perspective where I have argued that there is no Quranic warrant for the belief that the Arabs were descendants of Prophet Abraham or the Ishmaelites.
[2]The Quran ultimately remains the most authentic source.
I hope this helps, God willing.
Joseph
REFERENCES:[1] IBN ISHAQ'S SIRA OF PROPHET MUHAMMAD (pbuh)http://quransmessage.com/articles/ibn%20ishaq%20FM3.htm[2] ARE THE ARABS AND PROPHET MUHAMMAD (pbuh) REALLY DESCENDANTS OF PROPHET ABRAHAM? (pbuh)http://quransmessage.com/articles/are%20the%20arabs%20descendants%20of%20abraham%20FM3.htm