The reason why you find your front wheel going left and right is that is how you balance - it's an exaggerated version of what you do when you're riding along. A study showed that once you lock a bike's steering, it's virtually impossible to ride. Other factors, especially reduced gyro effects (tiny wheels), made for awkward but rideable bikes.
For your scenario of waiting at a light while being courteous to those that might be passing you (commendable trait, imo), I see a few possibilities on how to approach it:
1. Track stand - effectively you'll be putting your wheel in a turned position to begin with - so you sort of claim your lane before someone inadvertently takes it. However, you will move back and forth when doing this.
On how to trackstand:
http://sprinterdellacasa.blogspot.co...ackstands.html
2. Put your foot down - it's been long recommended to racers that they unclip and put a foot down at every stop sign and traffic light. It gets them used to clipping in under pressure (like at the start of a race) without thinking too much about it. (It also gets pesky racers to stop at legal stops instead of blowing through them and earning the wrath of various other road users). You'll find within 20 repetitions of clipping in that it becomes more second nature to you. If you're currently uncomfortable clipping in during stressful situations, practice first while stationary (repeat 10 more times after you think you have it), then practice in a quiet place (driveway, quiet street, empty parking lot). Your confidence and technique will both greatly improve. I'd recommend trying to clip in when the unclipped pedal is at the bottom of the pedal stroke - engage the pedal at a higher position, pedal it down, then press to engage (this for most normal pedals).
3. Lean on something. Not a car but perhaps a close sign post or something to that effect. You move the least using this method and naturally move to the curb, moving yourself out of the "travel" lane.
4. Time the lights - keep an eye out for the other light turning yellow so you can cruise through a just-turned-green.
hope this helps
cdr