Lol, it's more complicated than that, dont forget to include a counter weight spinning opposite the main station with equal momentum or you'll start tumbling again.
What do you mean? The dock at the centre of the ring will be able to turn at a different rate than the rest of the ship, spinning this part to the rate of the craft it's trying to connect won't require a counter balance. Once the ship is securely connected to this part of the dock, all you need to do ever so slowly put on the brakes. Using fuel for adjustments for these things is quite common. That's not to mention the on board gyros that help it rotate.
Oh yeah, and how do you propose to connect the spin section to the static section while keeping out the cold vacuum of space? You're gonna need some hella complex stuff.
I don't think you quite understand how the design works. Imagine a donut- the rotating craft, and inside of this donut parallel to it is another donut. This donut has ball bearings and can spin in another direction if it needs to, much like how the axles on a car can spin to allow the wheels to go round, and not have the rest of the car flipping with said wheels. All you need to do once the ship attached itself to the dock and once slowed down is to simply use the same mechanism the ISS uses to connect two craft together inside of this dock.
Suppose the space craft comes in with its nose into the dock. Once it spins in unison with the rest of the rotating craft, all you would need to do is to push forward the tube inside of the ball bearing donut to the hatch of the space craft.
But there's an even simpler way than this. If you have two ball bearing donuts on both craft. You can attach tubes to each other without having to spin together at all allowing for refuel and whatnot. Imagine a garden hose with a ball bearing screw tip so that you can spin the tube connected to a gas tank that also has a ball bearing connection with the tube.