Translating camera rotation correctly into quat from two different objects?

For a first-person camera I'm controlling the x rotation of the camera directly, but I'm controlling the y rotation on a parent object that orbits the player at a distance, this way I don't have to rotate the player capsule collider and it's safer for collisions. I'm trying to translate this to second skybox camera that rotates the same way, but when I look up and down, the skybox tilts, and I think it's because the W angle is not correct when I combine the two different object angles. Is there some way of stopping this odd tilting?

 

You really need to show us your exact setup of cameras.
What is your GameObjects hierarchy related to cameras and which scripts are affecting cameras. Otherwise it can be so many things.

My best bet is, you got angles/quaternions addition/ multiplications incorrectly.

 

There's a fundamental misunderstanding here, because the components of a quaternion are not angles.

If you're trying to do something in terms of angles then you can read out the (euler) angular components and use them to do what you need to do.