If you're going to nuke a hurricane, I would save it for a war with China. If it works (dissipates the storm), hey, good for them and hopefully good for combat operations. But a cyclonic storm is a heat engine, and you would be giving it a whole lot of energy, and the mushroom cloud comes from surface elements being swept into the pressure low. You could make it a more powerful storm, even if only for a short while. So, try it in someone else's back yard first.
As it turns out, it would probably strengthen it if it bothered it at all.
Hypothetically, there would be simultaneous eye wall detonations...no mushroom cloud because it's neither a ground level nor sea level detonation. (high altitude air bursts)
Somone else made mention to the addition of heat energy to the storm from the use of a nuke, but I am not so convinced such an occurence (or heat convection) would occur. In other words...I dont think the detonation of nuke is going to add energy to the storm.
Seems to me two different forms of energy release are occuring, hydro-thermal (hurricane) and, depending on the bomb, either fission or fission-fusion (nuclear detonation) Hard for one to piggy back upon the other.
It's all speculation, but it would be interesting to see if by some means of man we could disrupt the energy flow of the storm or at least disperse it by means of creating our own type of pressure wave to interfere with the storms convection currents.
It's all scifi, no doubt...but too bad we cant test it.
We're at the mercy of nature as always. I hope the storm looses strength and heads back out to sea to die, but such is wishful thinking...pray for those in its path.