Baoshan
So, I’m going with Boshan as a pretty typical unconquered Earth Kingdom. The’y’re not currently under attack by the Fire Kingdom, are aren't likely to come under attack because while Baoshan is situated at the ideal land route across the chameleon peninsula, its almost always better to just go around by the water.
Baoshan still keeps an active army, and like all of the other Earth Kingdoms, sends soldiers to serve Ba Sing Se's army, as they are beholden to the king of Ba Sing Se for their kingdom after Ba Sing Se helped defeat Chin the Conqueror.
Most people in Baoshan have the opinion that women are inferior in some way, and are definately too delicate to learn how to fight or to serve in the army. There are strictly defined gender roles outside of fighting too. For example, one of the few acceptable uses of earthbending for lower class women - called stoneworkers - is to fix things with their earthbending. Any lower class man who did the same job would be ridiculed. In the higher classes, however, stoneworking is something only specially trained male artisans are socially allowed to do.