Hello Chacora!
Between May, September and October, I would choose early October for your visit, especially since you are traveling with smaller children. The weather in October is still plenty warm enough to enjoy the Water Parks, but the humidity from the summer months starts to dissipate. You may run into a shower or two, but October tends to be a drier month than September. Crowds are low-to-moderate (save for Columbus Day weekend) as most families are in school during this time.
October also brings two very amazing Special Events to Walt Disney World:
Mickey's Not-So-Scary Halloween Party (MNSSHP) and the
Epcot International Food and Wine Festival.
MNSSHP is a family-friendly event with a special parade, fireworks, trick-or-treating, dance parties and special character greetings. We took our two small children last year and they were enthralled with it all and can't wait to go back again.
I hope this helps you make your decision, Charcora! No matter when you visit, you're sure to have a magical time.
Please come back and ask me any other planning questions you may have. I'd love to help you make this a vacation you'll never forget!
Pixie Dust,
Ashley