Here are some rainy day recommendations for both parks:
DHS
Book ADRs for both of your meals (You can spend the most time at Sci-Fi Dine In or Hollywood Brown Derby)
The Great Movie Ride (nice indoor queue and entire ride lasts 20+ minutes all indoors)
Gift Shops on Hollywood Blvd (they are all connected on the inside so you can go from shop to shop without going outside)
Club Disney on Sunset Blvd (new indoor DJ dance party located next to RnRC, great place to dry out and dance while your at it!)
MKP
Book ADRs for both of your meals
The Emporium Gift Shops on Main Street (all connected from the inside from one end of Main Street to the other all indoors)
Carousel of Progress (entire show lasts 20+ minutes in a seated indoor theater)
TTA Peoplemover (part of the ride is outdoors but you are covered from the rain)
Philharmagic (entire show plus the pre-show lasts 20+ minutes all indoors)
The Hall of Presidents (entire show lasts 20+ minutes plus the pre-show lobby is indoors and you can arrive as early as you want)
Indoor Rides with Indoor Queues (POTC, HM, Space Mountain, Buzz Lightyear, etc.)
Hope this helps! Good luck!