Thought about this over and over, so it's not just you. I don't really know. A lot was going through my head when it kicked out that first time. I still wonder if I hadn't countersteered would it maybe have corrected itself, but if it didn't and it kept sliding, then it would have put my girlfriend's side of the car into a wall. A lot of could of/would of/should of in this situation, but what's done is done, and the damage isn't as bad as it could've been.
First, don't second-guess yourself, because you can't change what happened.
As to the broader question that was raised, having had a lot of opportunity to practice driving a stick in less than desirable traction conditions (like half the year in AK), I would encourage all to remember when your rear-end breaks loose and is coming around, simply push in the clutch. Letting off the gas can create a compression-braking situation, particularly if your RPMs were high, and/or you've got tall gears. Clutching gets you back into a free-wheeling state, allowing your simultaneous counter-steering to straighten you out, and preventing your driveline from making your spin worse. Also, counter-steering almost always results in overcorrection and starting a spin the opposite way (which it sounds like part of what happened to you). Unless you've spent some time
practicing it, most people don't have the feel for when to come out of a counter-steer.
FWIW, every car I've ever owned has seen it's share of time in a snow-covered empty parking lot, doing donuts and slides. I even made both of my kids do it when I was teaching them to drive, and I make it a point at the beginning of every winter to take my DD out and do it again. Recovering from spins or slides is a skill, and like every skill, you've got to practice to hone it. Plus, if you do it enough, you can actually learn to use your throttle to help you in some situations (Think drifting a curve).
Plus, it's
fun! Just make sure you don't have an audience, and watch out for light poles.
I've even had a couple of cops show up. When I explained to them my
primary reason for doing what I was doing, and pointed out that they probably got the opportunity to do skid-pad training (if they say no, then you complain how the city's such cheapskates for cutting the law-enforcement budget so they don't get adequate training in vital skills--that'll win them over every time if you say it with enthusiasm), they've always let me go with a "hey, that's a good idea".
You can even do it with our cars if you get a fairly heavy rain.
Sorry to hear about your damage (and especially the ticket to add insult to injury). Glad that it was only metal that was injured, and that it turned out to be a good opportunity for an upgrade or two!