The descendants of Judah were called by the shortened name "Jews".  That is the simple explanation of how this name came into being.  Over the years, the term Jews came to mean all the descendants of Abraham, including all the tribes, not just Judah.  

The area around Jerusalem was the portion of Judah and Benjamin, and the Levites were active there although they didn't own any of the land.  The other tribes supported Levi to be the priestly class.  The rest of the tribes lived in the northern parts of the land.

After the division of northern and southern Israel, under the immediate descendants of Solomon, those who wished to follow the God of their fathers moved south from northern Israel into southern Israel, the area of Judah and Benjamin.   Thus, according to Chuck Missler, all of the tribes of Israel were represented in the area of the "Jews",  in or near Jerusalem.  

It is true that many modern Jews do not descend directly from Judah, but come from converts, notably in Khazariah.  However, these converts intermarried with Jews whose bloodline (DNA) went back to Abraham, so they are often mixed up.

I believe my deceased husband, who was Jewish on his father's side, and who was raised a Christian, had elements of both the "German" or "Khazarite" Jews in his ancestry, plus the more ancient Jews who lived in or near Jerusalem.  One can tell this, in part, by the names (first and last) on the genealogy chart which his nephew made while traveling in Europe, but there are no "sure things" concerning it.  I know he had Levite descent from his paternal grandmother.   

As I have discussed here before, I have the maternal DNA which goes back to ancient Israel through Ireland, but of course my mother was not purely Jewish.
She had the genes of many other peoples who flooded into Ireland, particularly (probably) the Vikings.  She didn't know she had this DNA, of course, nor did I until I received my maternal DNA from a genetics firm who invited me to participate in a study.  This maternal DNA will not descend from me beyond my son, as he has only sons, no daughters.  It is astonishing to me that an ancient haplogroup like this could persist long enough to reach even me and my son.  

So I am Jewish and many Doves are Jewish, in part.  When God told Abraham his descendants would be like the stars in heaven, He wasn't kidding.  We are everywhere.  So much for who is a "real Jew".

The other item of discussion which shocked you, Kimberly, is the issue of what Jews have done or not done to influence Western Civilization--ideas such as the negative ones of Henry Ford.  This is a separate discussion from the issue of who is of Jewish descent.  It is a thorny subject and wouldn't even start to discuss it in so restricted a space, and I doubt if I could give a complete answer even in a book.  I believe a lot of the things which are said are speculation, and cannot be
verified.  Only God knows completely.  We long for the time when the issues are resolved under the reign of the Messiah.