Contact Disney and let them know what has happened.....I've read of some very wonderful things that they have done for people in less dire straits than yours.
For example....perhaps they'll let you postpone your trip until after this 2 week period.....so the kids will only be disappointed that the number of days until the trip are a little more than they thought. I know that sounds odd to go on an expensive trip when you've just been laid off, but it's already paid for, and if you're not going to get the money back to use for survival, well, why lose the money and the fun! You'll need to work harder to be frugal about food....but you'd have to eat at home anyway, so just spend your home food budget on groceries at Disney and pack your lunches each day. TV dinners can be heated in the food court microwave. No it's not ideal, but hey, it's only food....and besides eating a sandwich in line means more rides!! You have little enough ones that I'm gonna bet you plan on having a stroller anyway, so carrying a soft side cooler should be pretty easy. Bring along water bottles or mugs from home and get free ice water at any CS restaurant.....bring along those little flavor packets ($1.88 for 10 at
Walmart) and the kids will think they have koolaid/juice. Hit the dollar store for Disney design crackers/cookies and they may not even care that it's not a Mickey Bar (ok, that's stretching it, but just remind them at least they're in Disney!!).
You will want to apply for unemployment as soon as you're done working....but around here at least you don't get paid for the first week you're unemployed anyway.....and here we "check in" either online or by phone, no going down to the offices anymore like the old days. You are supposed to be actively looking for work, but hey, if you read their list of how to look for work, one of them is networking with other people to let them know you're avaialble. So....tell people you're looking for work...you never know...the guy behind you in line might be a CEO of a small company in your town and offer you a job. Or go apply at Disney (though I hear they froze hiring). You can also read your local area job ads online and send out your resume from any computer......so apply for a few things. By the time they get back to you for an interview you'll be home anyway.
I would NOT however burn the bridge that is your current employer by telling them where to shove it and not staying the two weeks (tempting as that may be!). I'm guessing here, but sounds like you were told that your department or whatever is being eliminated and your last day will be x. Most lay offs, which is what the PP's are probably thinking of are "we are laying you off, get your stuff and go home and don't come back.". But not all lays offs are that way. Don't burn that bridge for a few reasons.....when/if the economy shifts again, you may want to return to that employer....burn a bridge and that's not possible. Another is that with so many people looking for work, prospective employers can afford to be choosy. Which means that they will likely contact previous employers of the top few candidates.....what your previous employer says about you could make the difference. While they aren't allowed to say a lot anymore, the one telling answer (at least for me when I was hiring) was whether you are eligible for rehire.....if you burned that bridge the answer is likely no. But if by chance they still say yes.....my next question is WOULD they rehire you if they had a position. That is likely to be no if you burn bridges.
If your finances say you can't make it to Disney after your job ends.....ask them if you can put your payments into another reservation 6 months or a year from now. Yes, it may be tough to take time off from a brand new job, but when that time comes around you can decide what to do....perhaps the new job is so good that you can afford time off with no vacation pay....or maybe they'll offer you vacation time without a waiting period.....or maybe you call Disney and explain and postpone again. The worst that can happen is that they say no to another postponement and you lose that money then....the best thing is that you don't lose the money you just have to wait and go.
I know if you have to cancel or even postpone, the kids will have a hard time understanding......and there will be tears and anger and everything that you don't need right now....you have enough stress and enough worries right? But...try hard to take a deep breath, put a smile on your face and help them understand that you're sad too, but it's not forever. They still won't get it very well, but getting mad at them is only going to add to your guilt tomorrow, lol. Lots of hugs....maybe bring out the surprises you had for them a little at a time over the next week.....go to the dollar store for some if you didn't have any.....and see how creative you and the kids can be to bring Disney into your house if you can't go there. Pancakes shaped like wobbly Mickey heads.....sandwiches cut with a Disney cookie cutter.....going to the park and pretending that the slide is Splash Mountain (bring along a squirt bottle, lol). It's amazing how easy it is to distract most kids from sadness with just a little silliness.
Good luck to you! May you find an even better job with lots of time off to visit the World.