Think of your childrens' safety first and foremost. If she's not a safe driver ("she has a hard time staying alert"), they should not go with her.
Aside from that, if it's her truck and trailer, too, she can make her own decision. If there's something she needs to know, show her.
If you really, really, really absolutely hate the idea of her going alone and she can't be dissuaded, then you go. And although I agree with you that the short duration of the stay is not worth the drive there and back, it is apparently worth it to your wife for some reason.
Happy wife/happy life, eh?
(This might be a good time for her to do some of the driving and learn-by-doing everything involved in hitching up, towing, unhooking and setting up.)
