Dear Dixiefiddler (a name would be better)
When you look at the passenger list(s) for Peter Burgwinkel don't forget to check out the following page which also includes great information.
For example for the 1927 Seydlitz ship, the next page notes the following under the column of the name of nearest living relative where alien came from:
Sybilla Burgwinkel in Bruck/Baden living on Flebacherstrasse. It also notes his destination as Clinton, MA which was the home of his uncle, Jonas Burgwinkel, 11 Beech St., Clinton, MA
In the 1932 General von Steuben ship list, the next page notes the following:
his father is Peter Burgwinkel who lives at Pfeiffergasse 3, Cologne-Poll. (Poll is a section of the city of Cologne) This is also a confirmation of the connection above to Jonas Burgwinkel because when you conduct a search for him on ancestry you will find his passport application when he returned to German in 1925 which notes he was born in 'Boll' which is undoubtedly Poll in Cologne. Don't forget to check out the next page on this document too so you can see a picture of Jonas Burgwinkel. There is also a family tree for Jonas on ancestry you will want to check out too: http://trees.ancestry.com/tree/9658232/person/-764872684?ssr...
Obviously, Uncle Jonas came back to visit in 1925 and surprise surprise, Peter decides to emigrate just two years later and where does he head to? To his uncle Jonas in Clinton, MA! But his wife, Sybilla is living in Bruck in the state of Baden.
Now that you know the towns and specific sections, you should have no problem pursuing your research with the local Standesamt (civil records office) in Poll/Cologne and Bruck in Baden. My guess is that your mom's half-siblings were likely born in Bruck??
Hope this helps,