padaddyof3...

First of congrats on your build..
There are different ways you can go on with the build..
all depends on the budget you have..
To really stop sound leaks.. as what I know.. and some one correct me if im wrong.. you have to re-do the inner walls and have them filled with some type of sound proofing material.. mineral wool or similar insulation.. or..
depending on the size.. you can build a room in that one.. building that inner room sound proof.. and making sure that all the sheetrock joints are filled in with silicon or backer rod.. to stop the leaks.. also making sure that in the original structure.. you dont notice any paths where there can be a sound leak.. such as electrical ducts, bad construction or anything..
Hopefully this helps.. once again if im wrong.. some correct me..