Depending on which level you are when entering TVHM, the game will adjust the enemies level a little. It’s not like in UVHM, where enemies scale to your level, but a little… Just to make the transition a bit more balanced.
Doing all missions in vanilla, and all dlc’s and HH’s will send you above level 40, and it will ruin your TVHM experience. It actually ruins your dlc experience in NVHM as well. Waiting until after TVHM main story is finished, is better, but not optimal. The benefits are that the enemies and missions scale to level 50, and you only level up to around level 54.ish. The downside to this is that now all your guns and gear are max level 50, and you enter UVHM at level 54. This is a brutal wake up call for many players, since even the top tier guns will start to fall behind.
If you have guns stashed away, that are on par with your level, then this is not a problem. You just use Clappy’s secret stash in Clappy’s Hideout and switch them, or you tough it out, and wait until you get to Sanctuary. If this is the first time you play UVHM, then you need to make do with what you have.
So, to sum it up… if this is the first time you play the game, and therefore also the first time for UVHM, then I strongly recommend that you leave the dlc material alone until you get to UVHM. You can start the dlc’s right away when you enter UVHM.
If you have access to gear at around level 54, then you can do the dlc’s in TVHM. As for NVHM… One or two dlc’s is OK, but you’ll be a bit OP in the early stages of TVHM.
Man, that was long winded… I think I need a beer now!