D&D is primarily about the epic adventures of great heroes (or equally great villains); that is the default expectation when someone says “we are playing D&D.” To wit, the game is about dungeon-delving and dragon-slaying. You can play other things with the system, but it’s not the default expectation, and the further you get from that paradigm, the less well the system is going to be able to help you.
Great people need to have at least enough mental health to, say, recognize reality, understand cause and effect, and at least try to plan for the consequences of their actions. Someone who is “off his rocker” is not a player character in D&D. Such a character is not capable of fulfilling the expectations of a D&D character, and the disruption you describe here is the inevitable result of such a character. The character never should have been allowed with that pitch, and should be retired now that the group has seen firsthand why it shouldn’t have.
The alternative option would be for this player to grow up, recognize reality, understand cause and effect, and plan for the consequences of their actions—namely, that they are ruining the game for everyone. They could “decide to react differently,” and keep their character in line for the good of the game—that is, they could avoid My Guy Syndrome. However, since it seems pretty likely that this character was chosen specifically to disrupt the game, I tend to doubt that this will work. Starting a new character will be far preferable—a clean slate, no baggage, no ret-cons. And a sharp, clean cut indicates strongly to the player that they have misbehaved.
To be frank, when you say “We still want the player to stay in the group,” I suspect you may be making a mistake. I find it very difficult to believe that this player was acting in good faith, no matter how much I remind myself that we should always assume good faith.