Ahoy there Swifty
Welcome to the game and the forum..or have you been here long already?
Thats good captaining to go out time after time. Early in the game you can run many back to back cruises without any the micromanaging you need later on.
Mutiners! Now thats not nice. Did you by any chance send the ship out with less than full rations? Its when the food is gone that the risk seems greatest.
Has any one else had a Mutiney ? How did it happen ?
As for a replacement Captian. You might be out of luck - depends on the episode/scenario/game you are playing. If you have a Captain it will by following the 1,2,3 below. This screenshot from my current scenario (Random Adventures scenario by TJ) it costs me a whopping $2,500 to recruit additional Captains but I do have a large choice which is nice. If you dont have another captain on offer, or cant raise the cash, then it might be start over time...or go back to a save position and be kinder to the pirates next time...nah..the scum...a few more rations will do it.

A Captain will wade ashore, gold in his pockets, parrot on his shoulder, hat still on. But only from a sunk ship - not a mutiney.
Good luck

Ps. Charlote? is that in the campaign series? Keep a tally on the medals/scores as you go along. You cant get them again after the event.