Melee 2 is indeed very weak - I'm surprised you survived the main storyline with that! Armour is pretty much essential for both yourself and your officers if you intend to go up against enemy warships as their crews will probably be as tough as Quelp. The German rapier is a moderately decent sword but the swept-hilt rapier is better, while the Hibernian, Polish szabla and Templar sword are better yet. For a truly awesome sword, go to Bonaire - you'll need to either moor at a beach and walk overland, or go into Kralendijk under a false flag, as Holland is hostile to Britain in the "Napoleonic" period. If your reputation is good, there's a man in Kralendijk tavern who may trust you with a problem, and if you help him, his reward is the best sword in the game. Alternatively, if you're near Port au Prince, sneak into town and try to find Angelique Moulin, who also needs help and the end reward may be a very good sword.
You earn relation points by sinking or capturing enemy ships. The ships which you can sink on behalf of governors certainly help, but so do any other enemy ships you find on the high seas. Look at your "Relations" screen and when the value for Britain turns green, it means you have enough points for a promotion. Then go and talk to a governor, whose dialog should then have a new option "I've heard I'm up for promotion."
You earn relation points by sinking or capturing enemy ships. The ships which you can sink on behalf of governors certainly help, but so do any other enemy ships you find on the high seas. Look at your "Relations" screen and when the value for Britain turns green, it means you have enough points for a promotion. Then go and talk to a governor, whose dialog should then have a new option "I've heard I'm up for promotion."