I don't know what's in the interlining agreement between NH and UA, but I don't expect that it would cover the situation your wife is/was in. I don't expect NH (or any other UA partner) would through-check bags to another flight, bought separately, that charges baggage fees. Had your wife bought a single ticket that included both legs, there likely would have been an upcharge included in the total fare to account for checked bags (and probably better seat selection since the international segment was in premium economy).