Sadly for your wands, stacking a Nullify and a Reverse Magic is of very little value. They will both trigger from a single Dissolve, and because they have red reveal costs you must reveal them both. At that point, you can chose which (if any) you want to pay for (and get the effect from), but they will both be destroyed because they were both revealed.
Also sadly for your wands, any face down enchantment will trigger Nullify. When your opponent casts an enchantment face down, you don't know what it is, and neither does your Nullify. It will trigger, and you must decide if you want to pay the reveal cost to get the Nullify effect, or just allow the spell to go through. Either way, Nullify will have been revealed and will be destroyed.
There is a new enchantment coming out in the next expansion (available very soon, this week probably) called Armor Ward that may help you defend your wands, but until then, my advice is to bring extra wands, extra spells to put on those wands, extra nullifies, and to stay more than one square away from your opponent if possible (Dissolve has a range of 1).