Rig Squishing Model Problem!

So I recently finished a model of a little boy in a jacket for a game. It’s textured, rigged and everything. I’m at the point where it’s time to weight paint it. Everything has been going peachy so far, except for this one problem.

 There are a few parts of the model that don't follow the bone as quickly and, while rotating, also squish around. I figured there wouldn't be many as I went through all the auto-weighted groups when I started, so I figured I could just move those bones less so that the players don't notice. I found so many parts like that to the point that it's ridiculous and I need to fix them. 

 I have no idea how. I've tried many things on the internet, but none of them were from someone who had the same problem as me, and no solutions worked. Does anyone know what's wrong?!

EDIT: The problem doesn’t really matter to me any more.

Auto weight tools are a good starting point you normally have to do some fixing to get the results you want. post some screen grabs…