Barrel straightening is a bit like straightening scaffold tubes. Not that I have ever strasightened a scaffold tube but I have straightened a barrel using the scaffold tube principle. Because of the safety implications, scaffold tubes can only be straightened by competent and authorised (?) people who have the right kit.
Identify the START of the bend. Identify the END of the bend - and mark. These are the 'anvil points'. Press at the centre of the area. Do NOT do ANYTHING outside this area because it ain't damaged there! MANY more pages and much more than that of course but that's a start
After it's straightened, I would stress relieve the barrel....