If you have a conversion that is halachically correct (beit din with shomer shabbos rabbis, mikvah, and for men circ) you are Jewish according to Jewish law.
The father's religion does not matter. If mom is Jewish, so are her children.
You said if the mother is Jewish and has children then her offspring is Jewish no matter if they become Atheists or Buddhists they are JEWISH those are your words.
In reading the Bible and the early church which at one point only had 2 types of People Jews and Gentiles. When Jesus was on earth as a Jew his family were Jews the Apostles were married and were Jews the Gospels were spread to many Jews through large segments in the world. Antioch was a very large Jewish city that believed in Jesus Christ as the Messiah, now I realize things changed dramatically when the early Jewish Church Changed to more of a Pagan Gentile matter, but that does not negate the fact that the offsring of many many believers were of Jewish blood so there is no way on GOD's creation that you have one inclination how to determine who truly is Jewish or Gentile that means Conversion is not accurate, unless you consider yourself an Atheist...