I think a lot of folks are ignoring the purpose of the potential flight. I agree that if I were moving, etc., that a single flight for the pet is probably worth the risk.
But the OP is looking to go home "for a few days". That's putting the stress of a flight on the dog twice in less than a week. Is it worth that stress for such a short time? Is it worth giving up control over your dog to the airline for such a short time? Will the dog be better off staying behind for a such a short trip?