Hello Anna and welcome to the Disney Parks Moms Panel, it's extra magical for me to be helping a Guest from my home County of Cornwall with their Walt Disney World Resort holiday plans!
It's never too early to start dreaming about your next trip to Disney and it certainly sounds like you already have 2 great months of the year in mind. A good rule of thumb is to try and avoid US National Holidays like Memorial Day which falls on 30th May in 2016 or Easter which is on 27th March 2016; it goes without saying the Disney Parks can become extra busy at these peak times.
Generally speaking mid April should provide beautiful weather conditions and would be super timing right after the Easter 2016 holiday plus coinciding with
Epcot International Flower and Garden Festival which traditionally is held each year between early March and mid May.
The weather towards the end of May really does begin to heat up and if your family would like to
take ewok on the wild side why not plan to attend
Star Wars Weekends which are usually held mid May to mid June.
Also for your added information; due to open sometime in 2016 is the exciting new Resort -
Disney Springs at
Downtown Disney!
I'm sure whichever month is finally decided upon you're sure to enjoy a magical holiday to Walt Disney World Resort making memories with your dear family which will last an entire lifetime.
Have a great Disney day.
~ Jane