A question of DLC and True Vault Hunter Mode

[Heroic Ryan]

I played through the game on a mechromancer and finished the main story at around lvl 35. I was a bit overleveled from playing through the Captain Scarlet and Torgue's Campaign of Carnage DLCs. I wish to do Tiny Tina's Assault on Dragon Keep, as well as Sir Hammerlock's Big Game Hunt, but I don't want to be overleveled for True Vault Hunter mode.

Also, I plan on starting a new playthrough. Should I just avoid DLC all together for the first playthrough?

tl;dr
Should I move on to true vault hunter mode on my main save or do the other two DLCs

And should DLC be avoided on your first playthrough

[z00t]

Yes. Start TVHM now. There is little point in getting further over leveled in Normal, which is capped at 30 mostly.

Pretty much yes, otherwise you will get overleveled. The Torgue one has some very strange leveling issues and you can end up with level 50 enemies in Normal mode. Good luck with that.

The longer term aim of any character should be to complete TVHM as close to level 50 as you can. It is a Very Bad Idea to start the third playthrough - UVHM at much over 50. UVHM enemies always scale to you. They are much tougher, have health regen, often have shields, and trying to take them on with underlevel gear is a Bad Idea. TVHM is capped at 50, so your gear will be that at best. Taking on something like level 55 UVHM enemies with level 50 gear will mean you have a very hard time of it.
It isn't possible to complete all of the DLC's in TVHM without getting horribly over-leveled. Selectively doing some of the DLC's in TVHM is not a bad plan. Which ones and when depend on your character, as there is some pretty useful gear to be had.