So sorry you got the message too late.
I would almost bet that if you show both itineraries at check-in they will tag your luggage all the way through. I've always found VN staff to be quite helpful.
If things don't go your way, after a couple dozen flights through SGN domestic I've never waited more than 20 mins for baggage to arrive nor spent more than 30 mins at check-in and subsequent security.
Also unless they have changed in last 12 months wear easy shoes to take off as all shoes must be removed and scanned at security. 👌