Well, I'm an officer's wife (not Army, but we've been stationed at Army posts). Certainly the Army post gossip gang would kick into mega-high gear over a general's reprimand. No doubt, if it were a small post, everyone would know what happened (or some dubious version thereof) and everyone would also know that general's family. This might result in some whispering about them, or some pointed questions for the wife while shopping in the PX. On a larger post - and some posts are huge - the family might not be that well-known, especially if they lived off-post, and so they would be pretty anonymous except at official events. So, the setting has a great deal to do with the effects on the family.
The repercussions for an enlisted son stationed elsewhere would be minimal. A lot of people would know about the reprimand (Army off-line communications work almost as well as the gossip chain), but the son's career would be unaffected...unless, by some unhappy accident, he reported directly to someone who'd been harmed by the general/father's actions, and that person turned out to be vindictive. Even then, I think the son would have recourse through his chain of command.
While I don't know many Army officers' wives, modern-day officers' spouses tend to have a lot going on in their personal lives (caring for family, careers, doing everything at home while the active duty member is deployed, etc.). Most of the time, spouses don't do those stereotypical teas, coffees, etc. you read about, because they are too busy with other things; if they do anything, it's to get together once in a while for activities that benefit the local community or involve the entire family. On a very small post, or an overseas post, the spouses do more activities as a group because the job opportunities are so limited.
Most of my fellow officers' spouses really dislike being excluded from events because of their husband/wife's officer rank. They also dislike being lumped into the "O-wife" category and the associated expectation that all officers' spouses are stuck-up and expect privileges. While some officers' spouses undoubtedly do ask for privileges or flout their spouse's rank, most don't. In fact, they shy away from discussing rank at all, because everyone treats them differently (as an alien life-form, or as a little tin god) when they discover that the active-duty member has a high rank.
Just thought I'd throw that in...might not help your story much, but it's based on 20 years of personal experience.