Hi Jeanne,
Your story's fascinating, but sadly Not unusual. So many families with Jewish heritage, for their own safety, changed their last names, their religion, etc., so as not to be tageted by racism & acts of hated. We did not walk in their shoes, so cannot judge them.
As to German surnames, many of them became Jewish last names too, as the German-Jew females intermarried w/ German men, or the German-Jewish men simply denied that THEIR last name was Jewish & simply said it was pure German.
Interesting your mom's last name was Weitzel! That was the last name of my "Uncle" George--a former L.A. motorcycle cop. He was not blood-related, but I adored him. In his case he was 1/2 German (no Jewish), 1/2 Irish.
If you can take an autosomal (auDNA / atDNA) test via FamilyTreeDNA.com, or via Ancestry, you could "compare" your Ethnicity % results against that other company---as now all of them have "refined" their work, to show more accurate percentages and of which ethnicities we actually descend from.
By the way.....POSEN, PRUSSIA, now Poznan, Poland, was a safe-harbor for Jews for centuries, until it wasn't, starting in about 1818, w/ a change in government that was anti-semitic. By 1848 huge numbers left Posen to elsewhere in Europe, or to the U.S., for freedom & safety. My own great-great grandfather, Julius Henry Fiedler emigrated to London, UK in 1838.
So your father's dad coming from there is a possibility of another line of Jewish. The thing w/ DNA though, is we might be 3/4 Jewish & 1/4 French, but have Only pulled the DNA from our French ancestors at the time of conception, & therefore only showing Percentages of French & other bits w/in those peoples' DNA. I don't show ANY of my 1/4 native American DNA--my cousins do!
Also in the U.S.--the histories of the American Indians, the Jews, & the African-American blacks have been "hidden", if possible--due to a wish to avoid serious consequences. In the case of the first two (Am. Indian / Jewish), you'll probably find almost 1/2 to 3/4 of Americans HAVE those ethnicities somewhere in their ancestry---it's just been hidden.
To me it's ALL enthralling as I love all cultures / all ethnicities--they just make our histories richer! : )
Anonymous (Spencer)