You can have the best shoulder mobility in the world, and it won't help if your spine can't extend.
A great way to approach core stability and coordination is to look at how the body works during gait.
Even if you have no aspirations to do back bends, a spine that can flex and extend properly will help you with the rest of life.
To mobilize the T-spine prior to more intense movement involving lifting, throwing, and even running such as intense sprint work.