Lexus 1999 RX Transmission

I bought this car 7 months ago from the Toyota dealer. After a month, the car seemed to be decelerating too rapidly when taking the foot off the gas, but not braking. I brought the car in and was told that this was an emissions issue and $700 dollars later the car was running smoothly again. After about 2 months, the same rapid deceleration began occurring. I again brought the car in and was told that the problem was caused by worn tires. $800 dollars of brand new tires, my car was returned to me. This time, however, the “problem” did not even appear to be fixed when I picked up the car. I drove the car again for about a month, and brought it back as the problem had not been “fixed.” This time, I was told that all along this had been a transmission issue and the whole transmission needed replacing, parts and labor $4500. My husband researched the Lexus SUV RX transmission issue and apparently there was an extremely bad run of these during this time period and that Lexus was acknowledging the problem and offering free labor on replacing these transmissions. After all of the different “solutions” and thousands of dollars, I don’t know what to believe and am leery of spending $4500 on a car I bought 7 months ago, on which I spent $800, twice to solve a problem that wasn’t solved, when this is over half the purchase price of $10,000. Is there a way to be certain this is a transmission issue, and a way to minimize the cost as this is turning into a black hole of car repair on what is, or was, basically a very nice vehicle.