Hello Mike,
If they were from Baden, Their records would probably be in Karlsrue archives. Unfortunately, I don't know where the records archives for Ungstein are kept. This is something you will have to find out, might help to know what religion they were as some villages were either catholic or Protestant. Yours I assume were Catholic as the Church was Catholic in Ungstien,
Ungstein is a small hamlet of Bad Durkheim in the district Bad Dürkheim in Rhineland-Palatinate. Ungstein has about 1350 residents and is located approximately 1 km north-east of Bad Durkheim.
Apparently had belonged to Bayern prevously.

www.ungstein.de

Bad Duerkheim
http://en.wikipedia.org/wiki/Bad_D%C3%BCrkheim

Bad Duerkheim District
http://en.wikipedia.org/wiki/Bad_D%C3%BCrkheim_%28district%2...

Rhineland-Palatinate
http://freepages.genealogy.rootsweb.com/~tqpeiffer/Documents...

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Ungstein, Micro filmed records are available from the LDS Family History Center closest to you for about $5.00. It would seem to have your family in them.

Germany, Bayern, Bad Dürkheim - Church records
Titles Kirchenbuch, 1640-1818 Evangelische Kirche Bad Dürkheim (BA. Bad Dürkheim)

Kirchenbuch, 1701-1829 Katholische Kirche Pfeffingen (Ungstein)

Kirchenbuch, 1701-1950 Katholische Kirche Bad Dürkheim

Kirchenbuch, 1726-1862 Evangelisch-Reformierte Kirche Bad Dürkheim (BA. Bad Dürkheim)

Kirchenbuch, 1760-1872 Evangelisch-Reformierte Kirche Seebach (BA. Bad Dürkheim)
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Kirchenbuch, 1701-1829
Authors Katholische Kirche Pfeffingen (Ungstein) (Main Author)

Notes Mikrofilm aufgenommen von Manuskripten im Stadtarchiv Bad Dürkheim.Parish register of births, marriages and deaths of Pfeffingen, in- cludes Kleinkarlbach, Kallstadt, Erpolzheim, Hardenburg, Leistadt, Weisenheim (am Berg), Herxheim (am Berg), Bad Dürkheim and Saline, Bayern, Germany. Pfeffingen is now part of Ungstein.
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ote 1720-1747 Taufen 1748, 1728-1744 Heiraten 1701-1746 Taufen 1740-1750 Taufen, Tote, Heiraten 1747-1765 Taufen, Tote, Heiraten 1766-1798 Taufen, Heiraten, Tote 1798-1829 FHL INTL Film
1050052
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I SUGGEST YOU COPY THE WHOLE FILM ONTO CD FOR FURTHER RESEARCH. and its easier to do your work from your home computer and addes in translation later, Fortunately or not its only one roll and won't take very long.
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This is in an area where you might find AMENT's / AMEND's as well. So please copy those records.
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Yes legally they were required to ask for permission.
Besides the Gov. Archives to find there immigration records, (If it was legal) You probably will need also to find the "Bistum" "Church Diocese" and or governing lord of the village. Which may be Roman Catholic Diocese of Speyer.

You should probably find the mailing list for the area, to ask the other researchers.
http://lists.rootsweb.com/

I hope this helps
Best regards
Kurt