I've been multiple years on Father's day (my anniversary weekend typically). Crowds are surprisingly pretty good. It is RIGHT before summer is in full swing and grad nights are winding down. The last grad night is the 19th. One year, Father's day was one week after Cars Land opening. The crowds were probably the lightest I've ever seen. It's possible EVERYONE was in Cars Land, but you'd think the general population would be increased.
This year, however, I'm a little concerned about the 60th Anniversary hype. Also Monday has always been the busiest day for us.