Amy,
I think you need to find out your "chocolate foot" and then try unclipping the other one until you become comfortable with standing starts at stop signs, traffic lights etc.
Chocolate foot as quoted from Team Estrogen website is:
let's find your "chocolate foot." Hans Rey calls the foot that you naturally put forward when you are out of the saddle, your "chocolate foot." You will have to ask him why. I use the term because I like the way he says "chocolate." Anyway, if you don't already know which foot likes to be in front, stand up and sprint for a moment, then while still out of the saddle, stop pedaling and coast. Look down. The foot that is forward is your chocolate foot. Still not sure? Find a nice stretch of linoleum, take off your shoes, run and slide in your socks like a kid across the floor. Look down. Once again, the foot in front is your chocolate foot.
Even though I'm right handed, I almost always start pedaling with my left foot. it might be the case with you as well.
Ihsan