What happens to DLC missions in the second playtrough

Solution 1:

The DLCs do reset so you can do it again. However, its beneficial on the second playthrough to complete ONLY the main storyline missions first, this brings you to a new mode called playthrough 2.5. In playthrough 2.5, all mission and rewards will be set to the max level of 50, so you'll gain much better unique weapons than if you completed them at lower levels.

You must not even accept a side mission until you reach playthrough 2.5 as the mission level is locked in as soon as you accept it.

Solution 2:

Missions do not reset in playthrough 2.5, only stuff left from playthrough 2 remains. That's why it not "3" but "2.5". DLC's also do not reset - if you go to DLC's right at the start of playthrough 2, those areas and quests will be of the level you first entered.

A couple more corrections:

• In playthrough 2, you are free to accept any side quests that do not have Unique rewards, as it helps to level up. Rule of thumb is - Uniques are blue, though not every blue is a Unique. After a couple playthroughs you will memorize them, for now here and there are lists.
• Loot will be the best once you reach enemies and quests of level 50, not playthrough 2.5 itself. Therefore, in playthrough 2 you are free to accept any side missions that are level 50, no need to go finish the game first - a level 50 Fibber will still be a level 50 Fibber.
• DLCs do scale to your level, so, similarly, you are free to divert to DLC as soon as (or shortly before) you ding 50, so you can reap all those pirate chests and Torgue fwap-a-booms at level 50 and go end the game with them.

A good example of OP stuff you can grab at level 50 while still on playthrough 2 is The Bee, the Fibber and the Sand Hawk.