velocity inheratance and force direction for gun?

ok so i have at this point, a highly over-engineered simulation gun for vr. and current ly im working on the projectile system. and the shell eject system.

my problem is i am having difficulties with velocity directions and inheritance. i can make the shell eject in the correct rotation and launch correctly away from the gun. but i cant for the life of me get it to always eject to the right of the gun. it is always launching to my right regardless of the direction of the gun.

so if i wanted to launch an object from the side of an object. and it always inherit velocity. and launch out of the correct dirrection what calulation should i do. im good at all kinda of math but i dont often do vector math