How do I return a cframe value relative to the rotation of a base object?

I'm having trouble understanding the wiki on this matter.

I'm trying to get a part inside a model to move to preserve the rotation of the model.

I'm trying to make a door that would open 90 degrees from its original position but is adaptable to any model orientation.

edit: I think the door example is misleading, what I want to do is get a part to always move to the right of the base part, I don't want to rotate the object, I want to move it so that it moves in a relative orientation of the base part.

Imagine one of those sliding doors in mall entrances, how would you make sure that those doors open properly at any orientation?