I built a cart for my rocket to move in and out of a KSP-style rocket building lab. I can stick the rocket to the cart when it's time to move it and unstick it when it's time to blast off.

When testing this rocket for the first time, however, I noticed when I landed back on Earth it put me on the ceiling of the lab. It seems like when the rocket is moved as a separate contraption, it doesn't move the initial position of the rocket controller to compensate.

Yes, it's supposed to do that. Otherwise it can create issues, but I will put something to change the landing pos later. I will come back to this post when I do it