If you're determined to travel during the holiday periods, though, book your vacation flights, hotels, and cruise far in advance. If it works with your schedule, fly on Thanksgiving Day or Christmas day; those are the least crowded days of the holiday season. And if at all possible, avoid traveling during weekends, on the days right before or after the holiday, and late in the day. It's not only crowded at airports but also northern storms can wreak havoc and create weather delays that cascade across the system.
From England I would say your cheapest and best late December destination with warm weather and reasonable prices is going to be Phuket. There are some other Thai islands that might be a bit cheaper, but they would be more complicated to reach, and they’d have fewer activities for the boys. Here are some Phuket resorts good for families. You can see that the price range is wide from cheapest to most expensive. In late December it’s peak season so you’ll pay at or near the top of those ranges.
Mid- to late-November welcomes warm, dry sunshine with temperatures of about 80 degrees in this subtropical Central American nation located south of Mexico. You’ll slip in before the holiday crowds and enjoy exceptional weather and affordable prices for tours and fine lodging. White sandy beaches, friendly native people, jungle adventures, and tours of ancient Mayan ruins await visitors on this small and easy to navigate paradise. Nov. 19 is Garifuna Settlement Day, a celebration of the Garifuna people, descendants of African slaves and native Carib islanders. All are welcome to participate in dancing, parades and tasting traditional foods.
Unfortunately I’ve only been to Cartagena in Colombia, although I know of some travel bloggers who live in Medellin and love it there. The mild weather year round is one reason people love it. I don’t speak much Spanish, which is a problem in much of Latin America, but evidently there is a pretty big scene of various expats and English speakers, so Spanish isn’t so critical. In other words, I like the sound of your idea and I imagine it’ll be great, but I haven’t been there yet so I am really not qualified to give real advice. Best of luck with whatever you choose. -Roger
Two other suggestions would be India or Sri Lanka. Except for a few beaches in Goa, neither of those attract the party crowd, and both are excellent for scenery and culture. India is cheaper as long as you minimize time in Mumbai and other big cities, but that is good advice for many reasons. Sri Lanka is a bit better organized, and on your budget it is good value and easily affordable. There are good beaches along the south coast of Sri Lanka, but India is probably better for beaches.
Since flights to Mexico City from the US and Canada are usually quite cheap this time of year as well, this could be a perfect short cultural holiday. This city has great shopping, dining, and nightlife, and the central historic and tourist districts are far safer than most people would expect. There are ruins just out of town as well, so a bit of everything is available.