If you want full control over the velocity and rotation, consider using a CharacterBody (or even just an Area) for the missile. When using a RigidBody, you should use apply_central_force() instead of directly changing linear_velocity.
About the rotation: Its usually enough to just rotate the visual representation (the Sprite2D or whatever you are using). To constantly rotate the whole RigidBody you should use _integrate_forces():
This is from the Using RIgidBody page in the docs. The example on that page is for a RigidBody3D, but you could adjust it for a RigidBody2D.
I realized that I shouldn’t have used a RigidBody. I was initially following the Your First 2D Game tutorial in the docs, and it uses that for some reason. Making it a CharacterBody2D solves it.