They have no right to ask for their investement back. They have offered to sell you all their shares for 400k within a week. You have made a counter offer, which they rejected.
You can give them a lower offer (370k, by the end of the year), but they can refuse.
Realistically, you might have to offer a bit more, as their investement has grown.
You can hit them with a suit if you want - they acted with apparent, but not actual authority. From wikipedia: "If the agent has acted without actual authority, but the principal is nevertheless bound because the agent had apparent authority, the agent is liable to indemnify the principal for any resulting loss or damage."
So you can ask them to pay you damages for anything they did without the right approval. You'll need a lawyer to do this.
You might want to ask them what charges they are thinking about making. There might be some minority investor rights they can sue over? But I'd ask a lawyer before doing this - I suspect this could force their hand, which you might not want to do.
Whatever the case, you want to buy them out, and make sure all the documentation for this is in good order.
On the other hand, you can sue him for acting as an agent without actual authority. Those hires and purchases he made that you explicitly vetoed? Invoice him, and watch him squirm. Tell him he can pay for them with some of his shares. But ask a lawyer first.
If he keeps making noise, ask him if you can speak to his lawyer. He doesn't have one. No lawyer would advise him to make such stupid decisions (trying to roll a CEO with just 20% of shares, vague threats, etc).
You have to buy him out eventually, or he'll be a recurring headache. It might cost more than 400k, as his investement has matured.