April MK Grad Nites are April 18, 19, 25 and 26th (and are only for HS kids/groups who bought separate Grad Nite tickets, with their chaperones, etc). ConcKahuna is correct about lots of the kids coming in from FL schools - you'll see lines (and lines!) of busses pulling in to the MK parking lots later in the day.
The MK will close at 7pm on those dates to get ready for the Grad Nite party that runs from 10pm
to 4AM. (Poor CMs!

) There also will be an early "Blast Off" DJ party for them from 8pm to 10pm, so if I was at the MK during that day I'd probably try and leave well before 7pm to avoid any transportation crowds.
You mentioned your stay was "middle of April" so just looking at the park hours for evenings on the 4/18 and 4/19 MK Grad Nite dates, it shows on 4/18 Epcot has evening EMH and on 4/19 Hollywood Studios has evening EMH so you might consider doing those parks on those nights
I
think I remember reading posts from last year that the kids really didn't affect MK crowd levels too much during the days - instead of hitting the parks most kids probably slept in most of the next day if they stayed overnight, and others just came in later the day of the party and left afterwards. But I might be wrong about that, and hopefully someone will post what they experienced! We were there a couple years ago during a Grad Nite weekend, but I don't remember anything but hearing fireworks going off at the MK for their party really, really late at night over at our resort
