Hello, Pheh Fun!
There are a lot of great options in both the value and moderate categories for a family such as yours!
Regarding Value Resorts, I'd first suggest you take a look at the brand-new
Disney's Art of Animation Resort, which includes Family Suites that sleep 6. This resort is having its Grand Opening on May 31st, however, so it may be difficult for you to get a room in early June.
Another great Value Resort that features Family Suites is
Disney's All-Star Music Resort. These Family Suites also sleep up to 6 and include mini-kitchens as well as two bathrooms. With three little ones on vacation with you, all of this will be such a wonderful perk!
At the Moderate Resort range, Disney's Port Orleans Resort-Riverside does offer some rooms which sleep 5, due to a trundle bed, which can accommodate Guests under 9 years of age.) At Disney's Coronado Springs Resort, some Junior Suites can sleep up to 6 guests, and include two bathrooms as well.
For my family, I know that having a mini-kitchen and / or two bathrooms makes all the difference in the world. While someone might not be quite ready to head to the parks in the morning, everyone else is happy while waiting, because they've already eaten breakfast. We also like to come back from a long morning / afternoon in the parks and make some snacks while everyone gets cleaned up for dinner (or naps!)
Please send more questions once you've narrowed down your choices, or once you've booked. I'd love to help you make this the most magical vacation for you and your little ones!