IME - The weather in April tends to be beautiful.
easywdw.com lists the crowd for those dates at 5's and 6's which is moderate. Pretty much all of April after the 6th is 5's and 6's.
As previous poster mentioned, it is a popular time for out DIS friends across the pond, but you shouldn't encounter too many US school vacations at that time. You would be after the Easter crowds (the week before will be VERY busy).
The flower and garden festival will also be at Epcot which is a nice bonus!