Hiya, Aklyon. I looksied at the links in your signature, thought I'd take a peek, and VOILA! I hope you don't mind me contributing with the power of Playerspeak while my character waits in the wings; I mean, it's not like I want these guys to get killed or anything, because that would throw me in the spotlight, so, truly, we both know I'm going to try my best to help. Ergo, considering how much effort the populace in the dome has given to militarizing and going out to make teh pewpew, I highly doubt they're going to take upon themselves the responsibility of saving a mining village. Besides, what if the mining village gets saved, yet the dome gets screwed in the process? Bad move. Unless this is the most badass mining village ever filled with dwarves, fey moods, and lava, you'd be screwed. Have Harlon get the miners required to rescue George and Nodachi, then see about replacing that antenna to get in contact with someone other than the Trader who's bilking this place for profit.
On the other hand, if that seems too inhumane, at least get more information about the mining village - how far away it is, how many people are there, all the supplies they have, and so forth - in order to make a better-advised decision. Alternatively, you could go for broke, get everyone killed, and have five new people attempt to somehow make the damn thing work.