I suggested that itinerary because of 14 days and your budget. You will either have to fly up to HAN or be on the move almost everyday.
Since you have only a few days before your VN adventure, getting a cheap flight SGN-HAN is not going to happen. Trying to get from HCM to HaNoi and back via road or rail in 14 days is just not feasible IMO.
You live in SIN and you can always fly back to VN. Why don't you see what you can of the South and save HaNoi & HaLong Bay for another visit? Or see if you can book a flight from HAN back to HCMC on the day before you fly home. If you can find a flight HAN-SGN, then you could include HaLong Bay. If you cannot book a flight, then I would forget the HaLong Bay & the North.
You do have the option of taking the overnight bus up to Hoi An (HA) from NT. Cut HCM to 2 days, overnight bus to NT on second day, 2 days NT, overnight bus up to HA on second day. 2 days HA, overnight bus back to NT on second day. One day NT, bus to Mui Ne the next day, 2 days MN, bus to DaLat. 2 days, back to HCM third day. This leaves you with a few days before your flight home to see the delta or tunnels, whatever you did not see when first in HCM.
As you can see, you will be spending much of your time on buses, or rail if you choose that option. Rail is safer than a bus, no question about that. The problem with rail is that you have to book several days ahead of time to get a sleeper or better class seat. I guess you could settle for hard seat and go the next day. I will let the rail fans advise you there. Here is an excellent resource for rail. Here is the best open tour bus option. You have to decide what is best for your trip.
My blog on DaLat covers several cheap places to stay. Same with Mui Ne. If you ride with Sinh Cafe, you can find both places easily. Both at $10/night. Or just chat with the moto guys that meet each bus. Tell them your budget and they will take you a place you can afford. Good luck.