Just had our first trip with ages 6 and 4 last month. I can only speak for Epcot and MK since those are the 2 parks we visited.
Epcot has many indoor areas....queues, rides, restaurant seating, etc. being inside (of course, the walking to and from different attractions will be outdoors so have your ponchos and/or umbrellas). Our children LOVED the escalators in the land and sea pavilions. I know you don't want to pay admission to just ride escalators all day...but if it's a particularly rainy time in the day, that will keep your kids happy for quite some time.
There's a Lion King movie in the land pavilion, a Crush the Turtle show in the sea pavilion, and several aquarium exhibits. This would be a great place to hang out in the rain.
There are several Magic Kingdom rides that our children liked that have shelter from the rain (both the queues and the rides themselve): Winnie the Pooh, Peter Pan's Flight, Small World, the Tea Cups, and Buzz Lightyear.
Rides like Dumbo, Magic Carpets, Carrousel, and Indy Speedway are rides with queues that are not sheltered much. I don't know how Disney does about wiping down rides after a rain shower (it did not rain on our trip)
, but I packed a Shamwow towel in my park bag so I'd have it if needed to wipe down these particular rides or benches for a quick rest, etc.
Another tip I found to be hand. Even kids ponchos are big for our aged children....so get those elastic head bands....not pony tail holders....HEAD BANDS to put around their waists when they're wearing the ponchos to "blouse" the ponchos up a bit so they're not tripping on them.
I bet it won't rain as much as forecasted.....just be prepared "just in case"....and then enjoy your magical vacation!