The villas are in Orlando. The OP said they might travel to Orlando instead of day tripping. For $600 a week, I’d consider spending a week in Orlando and a week at the free house in West Palm. You could easily hit Daytona Beach from Orlando. That takes care of 2 of the 3 things on his list.
Aside from Disney, there’s also SeaWorld in Orlando. I highly recommend Adventure Cove, but it’s really pricey.
I know it’s confusing, but “Palm Coast” ≠ “West Palm Beach.” Totally different cities.
West Palm Beach is considered South Florida, and is south of Lake Okeechobee on the East Coast. Palm Coast is north of Daytona Beach also on the East Coast, and just south of St. Augustine.
And Daytona sucks. There’s no reason you can’t have a perfectly lovely beach day at Palm Coast. It would probably be less crowded than Daytona and infinitely more pleasant. YMMV, of course. Did you mention when this trip is taking place? If it’s March or Spring Break time, avoid Daytona. It’s not really the hot trendy Spring Break spot that it used to be, but it would still be more crowded than usual.
Discovery Cove, not Adventure Cove. It’s not that pricey ($50ish) unless you want to swim with dolphins, and then it’s really, ridiculously expensive.
From the OP:
There’s no way to avoid Daytona if you want to get from Palm Coast to Orlando short of cutting across to the Turnpike, which is a really bad idea.
If you just mean, “don’t go to Daytona itself,” I heartily second that recommendation. Year round, actually. 
You have roads???
Animal Kingdom is my 2nd favorite park at WDW (after Epcot). The Studios is may least favorite, but has a couple of attractions that make it worth it (Tower of Terror & Rock 'n Rollercoaster).
I’d also recommend a trip to Universal’s Islands of Adventure.
I like Epcot and Animal Kingdom a lot as well.
To some extent, it depends on what you want to go to Disney for. Disney scatters its big thrill rides throughout its parks, and doesn’t have a lot of thrill rides to start with - so a thrill ride sort of experience pretty much means all the parks.
Magic Kingdom is “Disney” - its nostalgia. Its charming. Its also a little dated and most people outgrow it as teenagers - when its roller coasters are a little lame and its charm doesn’t appeal. But this is what people think of when they think Disney - Haunted Mansion and Pirates of the Carribean.
Epcot is “edutainment” - but has some of the best edutainment rides going - Mission:Space and Soarin’ It has some great shows back in the World Showcase. Its been described as a permanent World’s Fair.
Studios has some of the biggest Disney thrill rides - and a lot of shows. Like you, its my least favorite park, but we do need to stop for Star Tours and Tower of Terror. And now Toy Story Mania.
Animal Kingdom is a zoo - and more. The safari is my favorite attraction - we’ve had amazing encounters - a rhino and a giraffe so close you could have reached out and touched them…It also has Disney’s newest coaster.
I’ll add that you should probably skip Epcot if the kids are small. The best ride is Mission: Space, but it’s an extremely shaky motion simulator* and even if you don’t actually vomit you’ll feel like you ought to for at least an hour afterwards.
*Personally, I believe that the actual ride is secondary in causing puking. The problem is that they tell you you’re going to puke at least 30 times while you’re waiting in line and boarding the simulator, so by the time you sit down you’re already feeling queasy.
My kids always loved Epcot. Even when they were small. If we skip, we’d skip the Studios (and we’ve done Disney trips were the Studios takes an hour one morning to get there, ride Star Tours, and leave). But its one of those “every family is different” things.
We’ve also never puked on Mission:Space - nor felt like we were going to. And the “no spinny” section now is available for those that are puke prone.
What, you think your family is better because they don’t puke on rides? YOU THINK YOU’RE BETTER THAN US? I’LL TAKE YOU ON, YOU AND YOUR KIDS!
ahem
Sorry.
I don’t know why I said “if the kids are small”. It says in the OP that they’re 9 and 11, which I think means they’re tall enough for all the rollercoasters and they ought to enjoy Epcot too!
FWIW, April-May is a good time to visit, weather wise, but not a terrific time crowds-wise.
OK, keep in mind that I’m now a WDW (Walt Disney World) fanatic, so bear with me. 
Not only would I not commute 90 minutes to get to WDW, I won’t commute 15 minutes either. It’s an entirely different experience if you stay in a WDW resort hotel. Keep in mind that Disney has three tiers of resort hotels (Value, Moderate, and Deluxe), and even the Value resorts are fantastic. If budget is an issue, the Value resorts can be very budget-friendly, particularly if you figure in the cost of transportation, parking, etc.
I also don’t think that 3 days or even 4 days is enough to experience WDW, but that’s just my opinion. Note that besides the four main parks, there are also two water parks (Blizzard Beach and Typhoon Lagoon).
Back in the early '90s, I actually lived in Orlando for a few months, and took my sisters there on a 4-day pass. It was OK, but very crowded and not well-planned on my part. When I returned (at my wife’s insistence) in 2007 with my own family, we stayed on the WDW property, and it was a much better experience. In fact, it was the best vacation I’ve ever had in my life. We’ve since gone back just this last summer, and are planning another trip for next year.
Keep in mind that WDW is nothing like Six Flags or even Universal. If you want to get the most out of it, you need to do some research and have a plan. Here’s some tips to get you started:
My last few Disney trips have been business related - so I’ve been staying offsite. After something like 15 trips - I’ve discovered that offsite not only isn’t bad - in some ways its better. I’ve had great rates in some really nice hotels - nicer than the rooms we’ve stayed in at Disney (and we stay DVC or Deluxe). Theming isn’t there, and you have to commute, but with a car and a good choice in an offsite hotel - it isn’t a big deal - and the savings are considerable.
I went on the “less intense” version last year because my girlfriend wasn’t feeling well that day - I can tell you that it’s not a “no spinny” version, but a “less spinny” version. It was still more intense than I expected it to be, but mainly because I expected it to be pretty lame compared to the normal ride. I found that I still liked it quite a bit as it kept some of the G’s and weightlessness feeling.
Personally, my “skip” park is Animal Kingdom. It’s cool and everything, but I still consider it to be a half-day park. Hollywood Studios is a 3/4 day park for me. Magic Kingdom is a full day park and I’d live in Epcot if they let me!
My advice for Disney World: Have a plan.
As a Disney first-timer, you are wise to educate yourself as thoroughly as possible about what you’re getting into. WDW can be pretty overwhelming, and if you show up unprepared you’ll waste half your time wandering around (and at Disney, time is money!). So I have to chime in here to recommend the Unofficial Guide to Walt Disney World.
It’s packed full of unbiased information and advice about all four parks, lodging, dining, Downtown Disney (a huge shopping and dining district), transportation, etc., etc. There are also chapters on Universal and SeaWorld.
You cannot possibly see and do everything at WDW in 3 days, or even 4 or 5. (My wife and I spent 11 days there on our honeymoon, never left Disney property and didn’t get tired of it. But then, we’re geeks.) The Unofficial Guide will help you decide what you most want to do there, to prioritize and make the most of whatever time you decide to spend. And it’s a well-written, fun read.
My in-laws live in Palm Coast. It is a very nice area, though in my experience it’s nothing too exciting. I agree with those who say check out St. Augustine, and if you just want to kill a couple hours with a pretty drive, take a ride up and down A1A, one of my favorite roads in the US.
Good seafood can be found all over the area, but I love the Turtle Shack on A1A, south of Palm Coast Parkway and north of Route 100 in Flagler Beach.
And try to make that half day in the morning when more of the animals will be active. Especially if you take the safari tour.
The other bit of advice is to try to not cram too much stuff into each day at the park. Figure out what you really want to do and enjoy those things instead of trying to take it all in at once.
I can’t thank you all enough for all your input. You guys are great! I see that we have a lot of planning to do, but I feel confident that in our two weeks we can make it a great vacation and do everything we want to do.
Without the Dope, I probably would have never planned to see St. Augustine, nor would I have planned to take in all 4 Disney parks!
I’m still slogging through all this info and all the references to other sites. I can’t believe I thought at one time this would be a simple thing!
I’ll be glad to help you via PM with anything you need.
HH, regular reader of allears and regular listener of WDW today and who has ready every edition of The Official Guide and The Unoffical Guide every year for the past 15 years.