First of all, I hope you’re enjoying BL2 bruinlad’s link is a very good indicator on when to play the DLCs. Here’s some stuff about the various playthroughs (TVHM, UVHM et al).
You’re currently playing at Normal difficulty (NVHM). If you play the main campaign and side missions, you’ll finish in the mid-L30s. The final boss is L32.
After you’ve beaten the final boss, the game will give you the option to play at True Vault Hunter Mode (TVHM). This corresponds to “Hard” in a typical shooter. You can play the entire game again, starting with all your gear from NVHM and continuing to level up. Playing everything, you’ll end up in the low to mid-L50s. The final boss is L52.
After you’ve beaten the boss at TVHM the game gives you the option for another playthrough at Ultra (U)VHM. This is a “Very Hard” mode. Again you carry over your skills and gear but now the game always levels to you and enemies become significantly tougher. How close you finish to the L72 level cap depends on how much you play (farm) above the campaign missions.
If you don’t like grinding but want to hit the level cap, you can reset UVHM. This allows you to play through the entire campaign yet again at the UVHM level of difficulty.
Once you hit L72 you have the option to “Overpower” (OP). You will see Digistruct Peak on you fast travel list. This is a gauntlet of very tough enemies. If you fight your way through, you gain an OP level. You don’t gain more skill points but you will pick up OP gear which is more powerful than L72 gear. You can fight through the peak up to 8 times, each time gaining an OP level, up to OP8. Of course, it gets harder each playthrough. There is more to say about OPing but that’s an intro.
As for when to play the DLCs, you could play them on each difficulty. Moving to the next mode resets the entire game including the DLCs. However, once you hit L30 in NVHM or L50 in TVHM, enemies and missions won’t level up, so you get very little XP for your efforts. Consequently, I tend to play the DLCs after I finish the main mission in UVHM and they take me to the final level cap (L72).
If you don’t enjoy the harder levels, then I did the following for one character. I played through NVHM, chose TVHM and as soon as I got to a fast travel station, started playing the DLCs. You are playing them at the “Hard” difficulty but you haven’t had to play through the main campaign again and you get a satisfying amount of XP. There’s nothing to stop you returning to the main game after that.
That’s a lot of words but I hope at least some of them help