Responses
The problem is that so far the third prince has been building his faction and competing against 2nd prince but as the crown prince fell the throne basically fell in the lap of 2nd prince. With the biggest competition gone they are basically the top dog so suppressing 3rd princes faction and taking him out will be much easier. So in that sense politically it was better for them that the crown prince and his faction still remained in some form but sending the crown prince to the monsters territory means that he is finished with zero chance of comeback.
I don't get it. Why is the 3rd Price Council complaining about the 2nd Prince sending the Crown Prince to a dangerous place? Shouldn't they be happy that one of the Princes is out of the way?