Perhaps a really loose belt? When it gets wet it slips a lot and you have a large voltage drop from running everything instantly off your battery.
Other possibility is alternator going, if your splashing through puddle hard and fast enough, could have a alternator on the way out that when it gets wet takes a few min to then re "dry out" and work again. do you have power steering during this event? or does the AC stop working for those few seconds?
Could mount a Go-Pro in the engine bay if you had one to see the belt. My guess since their is the squeal something is going on with the belt.
2001 ZX3 2.0L Zetec-
Hatch Nation #42
Going through Rebuild See "The TICK Build Thread" for details (http://www.focusfanatics.com/forum/showthread.php?t=289168&referrerid=62897)