Fair enough, but look at the existing threads on the subject. Your sound insulation is only going to be as good as your weakest element. In your case, I think it is the windows, especially if they face the neighbors.
I'm not saying green glue and double drywall isn't a good product, when used as part of a full solution. I am simply saying you need to consider everything that may be causing sound to spill over to the neighbors.
Consider this as a water issue. You want to conver the family room to a swimming pool, but you have an open doorway where the water keeps spilling out. Making the walls stronger isn't necessarily a bad idea, but it makes no sense until you first plug up that doorway to contain the water. It is exactly the same situation with the sound escaping. And that is why my theater ended up in the basement where there are no real windows and the walls are backed up with a lot of dirt.
Of course, you then start going to crazy lengths to get that last little bit dealt with. Isolated HVAC, decoupling the ceiling, etc, etc. At some point you simply need to say "good enough", or if you are fanatical about it, you need to go all out, learn everything there is to know and build that acoustically isolated chamber.