I'm not gonna tell you to wear a poncho or rain coat.. I don't think that's what you came here for..
Like others said, protecting your valuables is the most important thing.
I don't know how long your trip is.. is it a one-day trip or a short trip? If so, you may be out of luck when it comes to the outdoor rides. If it's a longer trip, you could afford to save a lot of outdoor rides for another day.
You could still have a blast at the parks with kids. If you must choose a park, go to MK. It has the most indoor attractions. In Tomorrowland, the Laugh Floor, Space Mountain (may be too much for your kids,) and the Carousel of Progress are all indoors. In Adventureland, go to the Tiki Room bird show and Pirates of the Caribbean. Frontierland has the Country Bear Jamboree. Liberty Square has the Haunted Mansion - most of the queue is covered. Fantasyland has the teacups (covered,) Snow White, Peter Pan, Small World, Mickey's Philharmagic - just to name a few.
Also, keep in mind that you could walk through most of Main Street indoors. You could start at town square and walk all the way through the gift shop to Casey's (if it's really pouring.) To get to Tomorrowland, there is an area near the outdoor restaurant that is also covered (Lunching Pad?)