The Civil War is unlikely. The TLs when the Catholics/Arminians court Charles Duke of York and he unsuccessfully rebels against his brother, while Turtledove-nominated, are based on the "flanderization" of childhood bullying incident. I hope Henry has more common sence than this and won't push his brother into agreeing to this.
OTOH I can see him declaring war on Spain/Austria immediately post coronation, economic consequences be damned, which would be enjoyed by the support of Protestant nobility. Maybe even a continental intervention, earlier/stronger than OTL 1637 expedition.