Playthrough 2 (TVHM) re-scaling?

I finished Playthrough 1 at Level 37. Then I (accidentally) went into Playthrough 2 (True Vault Hunter Mode) and barely progressed beyond a few minutes of wandering around. I believe Palythrough 2 would then scale to the same Level 37.

Then I went back to Playthrough 1 and killed the Warrior a number of times for loot and then went to the Pirate DLC. Say after I finished all these, I am at Level 41 and then I go into Playthrough 2 (again) for all the missions proper.

• Will Playthrough 2 re-scale to my Level 41?

• If not, will the subsequent missions cathch up with my Level 41?

It is pretty boring already and not challenging with the Pirate DLC at Level 30 and not scaling to my Level 37.

Thanks in advance for your answers.