I believe that mulligans are only given on things that are the fault of the map - for instance, several maps can leave land nations on islands, or on peninsulas with only 1 or 2 land neighbors. Those are worth mulligans, as they are totally screwed up things that aren't the result of a player choice.
But on the other paw - events changing dominion, even to Misfortune 3, are generally the result of the player choosing high Misfortune, Luck, or Turmoil. Sucks to be them (sucked to be me, in a number of games
) but it's the result of their pretender choices.
No mulligan, in my opinion. Mulligans / starting over should only be the result of a very screwed up start cause by the map, not by the players.