"What about follow-up from this kind of incident? Should you correct the dog, console him, act neutral and crate him, or something else? And should you make the dog "be nice" to the person they just barked at?"

Correct? Depends. Did the dog take a chunk out of the relative? Did it lunge at the relative? Failing those, a NO, COME, SIT or PLACE might be enough. I, personally, don't care if the dogs want to avoid someone. They don't need new best friends, even if they might be relatives.

Act neutral? If the dog's actions got your attention, and you were made uneasy or don't want the dog acting out, then call the dog and have it follow your commands. Seems like you wouldn't want your dog to seem aggressive toward a relative, so you call the dog away, under your control.

Crate him? Why? If the dog is otherwise not having issues, and you control the dog, putting it in a crate might be a punishment, and a crate shouldn't be used as a punishment, in my opinion.

Something else? Put the dog in another room if it makes you more comfortable, or put the relative in another room, after all the dog is family and the relative is visiting.

Make the dog be nice to the person? Why? The dog doesn't need a new best friend. You are the dog's best friend. The dog is probably a good judge of character and characters. Why try to make the dog be nice?

I'm not a fan of trying to make my dogs like someone. Heck, I don't like most people, when it comes right down to it.

Probably bad advice but there it is.

Two cents.