You can do it, 12 miles is a very nice distance if it isn't too hilly. I have two campuses I commute to. One is 15 miles each way, the other is 18 miles each way. Both are relatively flat but my fitness is improving a ton. Sometimes I take a light rail with the bike if I'm exhausted.

I have two kids, 5 and 2 yrs old, and I don't miss out on much time since traffic in my area is crazeee and cycling adds maybe 20 minutes each way. But I'm in better shape than I'd be if I drove everyday, and I have more energy and MUCH happier than being stuck in traffic. So I'm a better dad for it plus it's one less set of car-related costs for our budget. But I'm in Cali and can commute year-round easily.

Dont sweat the bike too much. I ride semi-heavy steel touring/cyclocross bikes to work and since I ride 100 miles a week, my "engine" is pretty strong now and I pass or keep up with folks on road / aero tri bikes all the time (and I'm not trying to "race" folks on my commute). Ride what you've got, INVEST IN GOOD LIGHTS AND COMFY, WEATHER-APPROPRIATE BIKE CLOTHING AND LEARN HOW TO FIX A FLAT, CARRY A GOOD PUMP, and MAKE SURE YOUR BIKE FITS RIGHT SO YOURE NOT HURTING YOUR KNEES. Sorry for yelling, but that's the non-negotiable part of a 12 mile commute. Everything else is gravy and once you're a seasoned commuter you will be a better, more discerning shopper should you choose to get a new bike someday. Also, the best bike for commuting May not necessarily make for a good tri bike, but the engine (you) is the important part.

You can do it! It's often the best part of my day. Be safe and find the safest routes. Godspeed!