I have purchased plane tickets many times and never read the cancellation. Dumb, I know. But human. And thankfully, I have never had to cancel. My dad, however, bought a ticket to Arizona last year and purchased flight insurance. He had a medical problem that came and went, it was totally unpredictable. So he purchased the insurance. Well, about a week before his trip, he got sick. Called to cancel, they sent him a form for his dr. to fill out. The dr. confirmed that my dad had this issue and sent the paperwork back in. The insurance company refused to refund any of his money because his condition was considered "preexisting". So that kind of stinks. There probably was a condition in the contract advising that the insurance would not cover anything preexisting, but my dad never saw it. Was it his fault? Yes. But in his defense, you would think that if you are diabetic or something and end up really sick, they would approve that over an ear infection.
Anyway, best of luck to you...crunch the numbers and see if you can still go to Disney.

Seriously??? You should probably check your insurance policy before you ask your pede to lie for you.

Did the OP really expect posters would agree with her attempt to defraud the insurance company?

Yup, we'll be out a significant chunk of change, but them's the breaks. If you buy a non-refundable ticket with a hefty change fee to save money, you get a non-refundable ticket with a hefty change fee. Surprise, surprise. 
Argh! I bought tickets in late December for our August trip. Now we've had to spend $4K on waterproofing our basement after the Nor'easter...and it is possible that I may be out of work as of the beginning of July, because we were just informed that the law firm I work for is splitting up (and I am last hired!)
I'm not that stressed about the work situation yet, because I may still be kept on...but DH and I came to the realization this week that it is not wise to forge ahead with the August trip, especially because we just came back from a week in Arizona and need to get our ducks in a row financially...I figured we could change the tickets and hold onto our theme park tickets for a future trip (February perhaps)?? I can also get our hotel deposits refunded with no trouble, etc...
SO tonight I called Continental, and got the unwelcome news that to EITHER change our tickets OR cancel them, it will cost us $150 per ticket! This brings a $912 trip to $1500...there is no way we can swing that, but if we don't, we're out the original fares! I got a number to call for "Customer Care" but I doubt they will tell me anything different. I'm trying to figure out if flight insurance will cover this (we did buy it), but I'm really stressed meanwhile...and sad...isn't it bad enough we can't go, without them trying to make a profit off our misfortune?
Hoping this will all work out somehow...

Just an FYI - there are some insurance plans that will cover some pre-existing conditions. They are, however, more expensive. It doesn't help your dad any, but it is perhaps something to look into for future travel.




Just a warning about the credits (I may be misreading what you wrote). Generally, they are only valid for the person whose name was on the original ticket. So, you wouldn't be able to combine the four credits into two flights (for you and your DS) - you'd have to use the four credits to buy four tickets and the original four people would need to use them.
While I still don't think you have a valid complaint against Continental, I understand being frustrated with yourself and I do apologise for not correctly reading that is Delta (I'm guessing on a previous trip), who offered the flight credit.
One option is to cancel everything but the airfare. A significant schedule change (4 hours?) would give the OP an opportunity for a full refund. Some carriers will offer a refund for minor schedule changes.
SW doesn't always offer the lowest fares but they give you a full credit if your plans change.