I don't think that there's any question that it is water getting on your serpentine belt and causing slipping which will shut down the compressor. The first thing that I would do is shut off the car while it's in the car wash -- this will reduce the amount of water being sprayed into the belt area via the grill (no fan assitance, in other words). Then, keep the A/C off for a few miles and then turn it on. If it does not come on, restart the car. Repeat if necessary.