Hi there, Elizabeth! Welcome to the always warm and sunny Disney Parks Moms Panel!
I know most of my pals would tell you any time is a good time for Walt Disney World, and of course I agree. But as a lifelong Floridian, I can tell you that if you're looking for the best weather for a visit in April or June, I think April is probably your best bet. The weather in April has usually warmed up considerably, and the days tend to be mostly sunny. While we may get the odd cool day here and there, the highs should be in the low 80s and lows in the 60s. This Florida girl may still be a little skittish about swimming, but since you're coming from Maine, I bet it will feel like summer to you and your boys! By contrast, June is starting to get really hot and sticky, and you might see the summer rains start hitting in the afternoons.
I hope this helps you and your guys have lots of fun in the Florida sun, Elizabeth. Please feel free to visit us again if we can help you plan your magical Walt Disney World vacation. It's what we do best!
Kathy K.