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.
You can have the best shoulder mobility in the world, and it won't help if your spine can't extend.
To mobilize the T-spine prior to more intense movement involving lifting, throwing, and even running such as intense sprint work.