Not sure about which fighter ships are supposed to go first, or how that gets determined.
But the explanation for why Mace's capital ship gets so many turns is in the descriptions of his abilities.
In particular this one:
Fortune Favors the Bold 4 turn cooldown
Deal Physical damage to target enemy and all enemies affected by Target Lock, then grant all allies Valor for 2 turns. This ability's cooldown is reduced by 1 for each enemy struck. (Valor: Grant the Endurance 20% Turn Meter and reduce its ultimate ability's cooldown by 1 at end of turn)
What this all basically means in practice: Mace's AOE attack grants a buff to his fleet which speeds up Mace's turn meter. If his AOE attack hits 5 enemy ships (selected target plus all those which are target locked), the AOE attack can completely reset its own cooldown (almost like a fleet version of Lando's Double Down attack). Which means that he will soon use the AOE attack again and renew the fleet buff that speeds up his turn meter.
It's a mechanic that's deliberately designed to make Mace's ship go very fast, and be able to spam his AOE if he's teamed with reliable target locking fighters.
That is officially how Mace's ship is supposed to work. If there are any bugs affecting his ship, I don't know about them -- although I would not be surprised since the game has its share of bugs.
