The most important question here is whether the OP has a single ticket. If the two sectors are sold together on a single ticket then luggage would be checked through. If on different tickets it would not be guaranteed but likely if you were to ask the VN check in agent.

As per the reply above you would change from a domestic to an international passenger at SGN or HAN, and whether there is an airside transit route or you go landside and back through security behind check in depends on the layout of the airport.