Mid April the weather should be pretty warm
We did a trip 1st week of May and wore shorts to the parks and swam every afternoon. But 1-2 nights were very cold for us so I'd say throw in 1pair of jeans/sweatshirt for each family member
At the mods, you have the food courts so I wouldn't worry too much about packing food - you can buy almost anything you may need. When we stayed at PO a few years ago with a 3yo & 1yo we paid for the refrig in the room to help with drinks - kept milk in, etc. Have you thought about shipping down your childrens' favorite items ahead of time?
There's a really good packing list on Mousesavers.com (very comprehensive).
Have a fantastic time!!!