If it will be a summer trip, then bear in mind how hot/humid places will be. Florida in the summer is really humid, for instance, Dubai (which is my idea of hell in any season) will be 40 degrees +.
Okay, so two autistic kids, 14 and 11 who won't enjoy anywhere too hectic and busy and you'll require downtime in summer for £16k. You could very easily spend that in California, which we did with our kids at 10 and 13. They LOVED it. We did a mix of cities and national parks, but it can be a lot of driving, depending on the itinerary you choose.
Costa Rica is supposed to be amazing (we're going later this year, so I can't comment on that yet), but for kids who don't want hectic it might fit the bill and you can keep your trip to say three different places to reduce driving time and increase chill-out time. It's the safest place to go in Central America and very popular with Americans, so quite clean and sanitised.
If nature would appeal, then take a look at South Africa, Namibia and Borneo as well. We have friends who've been to all three and raved about them.
If you're going to do a big trip over the summer though you will need all of that budget. The flights alone could well be £5k or more before you add in hotels, car hire, excursions and food.