Pretty bike! Congratulations!
Personally, I wouldn't have started off with clipless on a new road bike (unless you've ridden one before, which you may have mentioned and I'm not awake enough to catch it). Anyway. You don't need to unclip both feet when stopping. It delays getting moving again, because you've got two feet you've got to get into the pedals. Yes, you will unclip one foot and then lean the bike in the wrong direction. It happens. You will eventually learn not to. Like Catrin, I had to make a mental list of what to do to stop smoothly: "Back brake, unclip, front brake, get out of saddle, lean bike, foot down." Eventually, it became second nature, and the pauses between these got shorter...and now it's become "back brake, front brake, unclip." I second Catrin's suggestion--go out in a parking lot or a field. Pick a foot (I'm right-footed), and try to consistently stop and unclip only that foot.