I'm sorry but i got to say you don't have much experience driving cars hard, while better cars WILL make you faster, you should be able to take a corner of your description.
Learn counter steering, weight transfer and get a feel on the car, most modern cars, even sport cars, lack a proper feel. If you want a new car to learn with i suggest GT86 from Toyota, excellent response from the chassis i hear. Doubt it's anywhere near what the car's icon was, but closest thing to the real if you want a new car.
Not sure what's tight roundabout in your sense, and were you trying to go full 360 on it, or straight, or a 90 degree turn to the right, ie. the first out.
Now, go and do the same on snow (with STUDDED tires also containing friction ribbons or whatever they are called in english) and take it at 80km/h entry speed maintaining at least 60km/h exit speed if you are taking first or going straight.
Better yet, take a small, nimble, agile RWD car to a track day, you WILL have a blast while learning to drive better. Just start slow and at each lap go slightly faster. At the go too you could take it to a tiny autocross setup and learn dynamics of grip and weight transfer.
But you are absolutely right, regular cars have a boat feeling to them. I got gifted a Calibra as a daily driver, it's sufficiently old that it only has ABS and very low fuel consumption so i use it for daily driving etc. while my proper cars are at garage, it's absolutely terrifying experience at any speed above crawling when exiting corners, being automatic and FWD. Fortunately i'm going to use for the winter my '83 Corolla with a '97 1.6L 20valve VVT-i engine, roll cage, heavily modified suspension, heavily stiffened chassis with about 160whp and now that i finish this round of upgrades HOPEFULLY weighing in at just 840kg :)
The next model of that car is still the best in F-group rally. Shares same chassis bottom plate even, almost everything can be just bolted in from the next model to this older model, but this older model as Sedan model is some 150kg lighter from the factory.