So you were able to launch the DVD disc by opening its Video_TS folder, that's great
Now that's how my test went :
* The DVD menu was playing in VLC, with an option to "Play All scenes" (we need to start at 00h00m00s)
* It started to play the 1st chapter, I paused it quickly (let's say at 00h00m03s) then dragged the slider totally to the left (while Paused), to rewind to the very beginning of the movie (00h00m00s)
* Now you add your external subtitle .srt file (Video => Subtitles Track => Open File... it opens the dialog box, right ?)
And now we're facing "2 steps which probably need to be improved" because :
1) The sync isn't really accurate (for example, if the 1st subtitle is expected at 13s and it displays at 15s then something is wrong)
How do you know it is expected at 13s ?
By opening the .srt file using NotePad, and reading it starts at 13s (.srt file is a simple text file)
How do you know it appears at 15s ?
Because Vlc clock shows you it appears at 15s (instead of 13) and what you hear is not what you read.
2) If you drag the slider (to move quickly within the movie) then no external subtitle appears anymore and you'll have to do all this again.
Now maybe I got those 2 issues because of my slow PC but I'm not sure it's the cause...who knows, maybe all will work at your place fluently, in case you got the right external subtitle file ?
This being said, if Vlc developers think there's something to improve in this, maybe they'll find the test interesting . If I understand well, VLC_help thought it was impossible actually to add an external subtitle file (as the dialog menu didn't open) . Maybe this test shows it's possible to get the dialog menu, using the 2 "special" openings described in the precedent post. I'm sure he'll do his best (when he got time) to see if there's something to improve and maybe help you solve your issue.
But don't forget this point : you won't easily find external subtitles that will perfectly be in sync with your DVD.
If the subtitles were'nt initially included in the original DVD you got, it means someone prepared them by himself, maybe after a DVD rip, so there are chances that the sync will not be perfect with your DVD
Anyway, good luck and I hope you'll make it