One of my ancestors was also from Baden, but farther south, in the Schelingen district -- Vogtsburg im Kaiserstuhl -- much closer to the Swiss border.
Standing armies were generally not the norm until modern nations came about -- too expensive to maintain in the long term. Usually the general populace was conscripted and mobilized as need arose. If you read about the Grand Duchy of Baden here -- http://en.wikipedia.org/wiki/Grand_Duchy_of_Baden
-- there is a note that during the 1848 revolutions Baden was one of the centers of revolutionist activities, with its short lived republic suppressed mainly by Prussian troops (probably at the request of Duchy nobility).
In case you had not heard of it, you might be able to find more info by visiting the State Archives of Baden-Wurttemberg website at: http://www.landesarchiv-bw.de/web/49812
This page is in English but most of the rest of the site is in German. Google Translate will be your friend. Go down under "Archival Department" to "Gerallandesarchiv Karlsruhe" and click it. (Karlsruhe is the archives administrative region for Reilingen)
Some resources there might help you research the military history:
Click the + on the folder "Neuere Bestände (vornehmlich ab 1800)" [Newer Collections (Mainly from 1800)]
Then click the + on the folder next to "Krieg" [War] to expand that. I haven't delved deeply into it, but there appear to be something like regimental histories in there.
Hope that helps!