A chicken coop really should not smell - it is only when things are out of balance somewhere that an odor develops. You said this mostly happens after it rains - can you address where the leaks are to prevent the water getting into the coop?
Other things to address are:
Population (how many birds to how much space. If the coop is too small for the number of birds it houses, the poop will build up faster than the bedding can absorb it)
Bedding - what kind and how much. Some people use shavings, others swear by pine pellet bedding and still others use sand. What you use is as much personal preference as it is geared towards your environment. I am currently using shavings which absorb the poop really well. I've also used pellets and liked them a lot too. Until you get your leak issue resolved, you might also try getting a product called Stall Dry which is in the horse section of your feed store, and spread that around - it helps to dry up moisture.
Ventilation - if you are smelling an ammonia smell, you might need to look at your ventilation and see what you can do to increase it.
I know none of those things addresses your immediate question, but an ounce of prevention is worth a pound of cure or so they say
Regarding cleaning it now, I would scoop everything out of there and then put down a layer of stall dry and then some dry, clean bedding on top. I'd also consider installed poop boards so you can more easily clean out the majority of the poop without having to scoop the whole coop each time. And I'd definitely address the moisture issue when it rains.
Good luck!
