Not too sure about the specific wet weather.... but "Round-up" is great for getting rid of everything... I wouldn't worry too much about a bit of rain, issue is with "run off" - heavy downfalls will affect it, but a drizzle / light rain should be ok... I've applied this in wet weather before & did it's job...
Gallup or Touchdown will do the same job as Roundup but at half the cost. Personally wouldn't spray if I knew there was rain on the way - the weeds need to absorb the weedkiller for it to work properly.