Best way to dissolve caramelized sugar
Walk away.

No, really - it works.  Once you add the water to the sugar, it will likely harden and clump up (I don't know how to stop that happening).  But once it does, you can just walk away, and leave it to sit till it cools down.  

A lot of the sugar will just dissolve on its own, given time and enough water to dissolve into.  Some mixing (occasional stirs as or after it cools) will dissolve some more.  And at the last, when most of it has dissolved, you can gently start heating the pan up again, stir it around, maybe bring it to a boil for a bit, maybe add a bit more water and heat some more to get at those last undissolved chunks...  

It's sugar, in water.  It will dissolve until the water's saturated.  It takes time to dissolve on its own, and that's annoying if you want to use it right away - hence measures like heating, or stirring, or crushing the dried caramel to stir into water that way.  But it really works just as well, and is less tedious, just to give it some of that time and let it dissolve away.

I did this when making a caramelized burnt-sugar syrup, and it worked.  Adding the water was pretty spluttery at first (the caramelization had to be stopped pretty fast), but I did notice the caramel hardening to the bottom of the pot once it had settled a bit.  I gave it a few stirs, and walked away to take care of something else - and by the time I got back to it, most of the lumps were well on their way to dissolving.