Transmission fluid in the radiator

It seems to me the mileage and age are too low to be having this type of problem. The exception would be if the coolant is still original. It needs to be replaced every two years to prevent a build-up of harmful acid that attacks the metal parts in the cooling system. There are water pump lubricant, seal conditioner, and corrosion inhibitor additives in antifreeze to prevent these problems, but it's those additives that wear out in about two years.

All of the charges you listed seem too high, so I'd recommend getting a second diagnosis and opinion from an independent repair shop. We know a new radiator is needed, along with new antifreeze, but if this just occurred recently, you will likely get by with a transmission flush. When antifreeze finds its way into engine oil or transmission fluid, it will melt the soft first layer of engine bearings and transmission bushings. Either of those will lead to a major failure, but that damage doesn't occur right away. When engine oil or transmission fluid gets into the cooling system, it will slowly rot the rubber radiator and heater hoses from the inside, so this would be a good time to have the cooling system flushed too.

The common maintenance procedure for cooling systems is to drain and refill the system every two years. Many mechanics prefer to perform a more thorough flush the first time this maintenance is done to clean out the casting sand that is usually stuck inside from the engine manufacturing process. After that, drain and refills are sufficient if there are no other problems.

Every manufacturer also lists a recommended service interval for automatic transmissions. Most of the time we do a simple drain and fill which removes about half of the old fluid. The filter gets replaced at the same time. The new fluid has enough additives, so it's not necessary, or even possible, to get all the old fluid out. That is what the more-involved transmission flush is for. That is what is needed here to be sure all the antifreeze has been washed out. The flush also cleans everything out of the cooler lines that run from the transmission to the radiator.

You haven't listed any symptom that would point to the need to replace the thermostat. For the price you were quoted for that repair, the new thermostat must be made of solid gold, or this car model is extremely difficult to work on. A lot of models today require special transmission fluid formulations, and some of them are pretty expensive. Other than the cost of the transmission fluid, I suspect you're going to get a much more reasonable estimate from an independent repair shop.