We stayed at the Polynesian because it's equal walking distance to the monorail (to Epcot), to the private boat that goes from Polynesian to Grand Floridian to Magic Kingdom, and to buses to other properties. It's pricey but you don't need a car. We had 2 older kids and then a baby, so we came back from the parks at 2-ish for naps, sent the big kids to the pool with one adult, and then hired a Disney sitter for the baby so the rest of us could go out on the "big rides" and a real dinner.
Get a small fridge so you can keep snacks and things like cheese and yogurt on hand. You'll be paying for all your meals, but you won't be renting a car or spending forever trying to park and take the trams. A lot of people I know have rented a villa on the property as well - that give you the kitchen and your own breakfasts. We always took a small soft-sided cooler or insulated bag with us that had snacks - you can take your own food onto Disney properties/parks. That means no waiting in line at key meal times - if you're happy to eat a PB&J sandwich. We bought some supplies at a market on the way in - get a paring knife (for fruit), some plastic silverware & paper or plastic plates, and a small bottle of dish soap. Get a few extra hand towels to use for draining or drying clean dishes. The advantage to having snacks on hand is that a hungry and cranky kid standing in line can have a little something to tide himself over.
Definitely take refillable water bottles - don't waste your money on plastic bottles of water you pay for. I think that's the biggest marketing scam around (and not just at Disney).
I agree about Birnbaum's book - it's updated frequently. One of the great tips we got from it was to enter the park and proceed to the far end! Yes, you have to drag kids past the first few attractions, but everyone will be getting on those lines. Instead, we went to the back of the park (with virtually no visitors), did those attractions, and worked our way back to the exit. Then when everyone was fried and exhausted, we were nearest the exit for either the boat or the monorail or even the bus.
You can certainly do a VRBO but the Disney properties offer pools - the kids can only stand in so many lines, and sometimes you just need to come back at 3 PM and let them swim and go down a few water slides.
You can use a travel agent, but if you are a member of AAA, use that service (sometimes they have info on coupons and so on). Or use the Disney travel coordinators especially if you are booking things like character breakfasts. If you're on a budget, tell them - there are properties in a variety of price ranges, the most expensive ones being closest to the parks. But you also need to decide which parks you are going to visit - there are quite a few appropriate for this age range, and they cater to different interests.
You can also consider having one set of parents keep both kids on one evening so the other set can do something "adult" at the parks, and then switch off a different night. There are a lot of options for adult entertainment.