Yeah, definately get yourself rain gear, and try to to stay away from yellow to avoid mixing your children up with other children in the midst of a pop-up rainstorm.
The day can start off beautifully, but the humidity builds up quick, (we're talking heat index can average 105-115)and I'd say around 3pm everyday, you're going to get rain. But it's not so bad, it's a great time to take a break, catch a show, wander around Innoventions, or eat a meal. And USUALLY, the humidity goes way down after the rain, and although it will usually work back up, it's fairly nice and almost comfortable after the rain.
If the rain is more than a couple hour deal, I would say to stay away from AK, there's just not much coverage there. Epcot is good b/c there's a lot of indoor longer attractions/exhibits (Living Seas, Innoventions, Imagination). MK has a lot of indoor attractions too, but you'll mostly have to get to each by facing the rain. The Studios is OK, lots of indoor/covered attractions/shows.
You can always go to DisneyQuest, or just go from hotel to hotel, me and my friends LOVE doing that. Check out the different gift shops, arcades, pools (as long as it's not storming..well..you're already wet from the rain, right?

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