Could it be possible to allow player fighters and bombers to dock? It could work like this: The player in the fighter clicks on the other player's capship and clicks "Dock." The player in the capship receives a request to dock just like a trade request or a group invite, which he either accepts or declines. If he accepts, the fighter may dock, repair, and buy ammo just like a normal base only without a bar, commodity trader, and ship dealer. The fighter may return to space at any time. (Unless he reenters a battle, which is against the rules.)
Note: A player shouldn't be able to quit on the battleship and continue later, because A) He'll leave the ship in a different place from where he started, leading to potential abuse. and B) The capship commander might need to make room for other fighters. So if the fighter leaves, he'll resume in space.