first off - good move practicing at home, this is a tough lesson on the side of a busy road in the rain.
second, get some good tire levers for yourself. with some of my tires i am shocked at just how much force i need to put into the levers to get the initial bead off the rim, once you get it started you'll be good to go.
look for tire levers with a solid profile that will not bend. spoke hooks are nice, but not necessary.
insert one lever, hold it against a spoke, insert the next lever about 3" away from the first, lever it down and push away from the first lever.
practice makes perfect.
finally, (while this wont help on the side of the road) a little soapy water will help tremendously.