How should a country respond to sudden market instability to restore growth and investor confidence, and what if the country depends heavily on Bitcoin and the code is compromised allowing 15 million extra coins to be mined?

I'll answer your question in reverse:

To put it simply, the limit of 21 million coins is hard coded. Is this is to be changed, every one has to agree to it, without it, not possible. User-13568161252778373682 sums it up well what a hard-fork would be like.

Though the adoption and usage of Bitcoins is doing well, for any regular sized county, it would be hard for it to be dependent on Bitcoins. If a country is seeking alt. currency, they would have much better luck defining their own and managing that, something that can be done very easily with Ripple.

Instability has so many issues, historically, governments are very afraid of flight of capital. The usual knee jerk reaction is to clamp it down, which makes the money go underground and into suitcases, i.e. the flight of capital increases. The more a government clamps down, the more of an issue it becomes. I am no economic expert, perhaps someone else would be able to shed a better (educated) perspective on this.

Instability usually arises from government actions. Fix the government and you calm the storm.