In general, job traits do not "stack". The higher tier of Dual Wield from NIN main would override the lower tier version from your sub. None of the other job traits in this game stack, so there's no reason to believe Dual Wield as NIN/DNC or DNC/NIN will either.
Lyonheart, like Eorzia, will be reborn in FFXIV!
FFXI veteran (Lyonheart and Lakiskline of Lakshmi)
1/467 on signed HQ Weskit!!!