That kit would do it. The radiator drains I run across on lots of makes often fails to drain. Gelled coolant and swollen rubber seals can stop them from draining. On the short 6 engines to fill block you can slide the pinch clamp up on the short hose from rad to the trans cooler on left (driver's) s...

The cooler line fittings are different and are plastic pipes with a squeeze to unlatch fitting. You will have a hard time getting to the fittings as the cooler is not in radiator but is just bolted to it with external coolant hose connections. Drain and refill is easy on that car. You need a TX 40 a...

There is a misconception that all the trans fluid needs to be replaced at once. That is only needed if there is some sort of "poisoning" of the fluid. 82000 miles is not in the range of big risk but if your transmission has some deposits on sealing surface and the rubber seals have hardene...