The least expensive from DC area is going to be Dulles straight-shot to Cancun. It is 3 hrs. 20 minutes and you can find very reasonable rates, I'd say $250-$350-ish for a ticket. Do NOT stay in Cancun - pick a hotel in your price range in Riviera Maya or Playa del Carmen areas. These areas are much more charming and beautiful compared to Cancun. Search for reasonable hotels/resorts with good ratings on tripadvisor.com
I personally don't love all-inclusive resorts, but many people do and there tend to be some pretty amazing deals if you buy the vacation as a package this way. You also don't have to worry about how much you're spending every meal while there. Another option is to not do all-inclusive and stay close enough to Playa del Carmen to go into town for some meals. It is a very quaint town with an almost European feel to it, and you can find reasonable prices for meals.
I promise you and your family will love this area and the people!
If you're willing to spend a little more on plane tickets, Costa Rica is also fantastic - but will be more $ overall.
Have fun whatever you decide
