The Park Royal in Cancun located on the Cancun strip is advertising their Ambassador Suites that accommodate 6 people as follows:
Ambassador Suite with 3 double beds • Living/dining room • Cable TV • Terrace • Jacuzzi (Max occ,6)
KIDS 2-3 YEARS STAY, PLAY &EAT FREE when sharing with two adults. Just pay a special airfare!
From my experience, I think it is difficult finding a resort with rooms that will allow 6 people. They do exist but just harder to find one that is available in the place or timeframe you want to travel. You didn't mention the ages of the 4 children. Perhaps there is a resort that would have adjoining rooms....one for the children and the other for you, depending on the hotel policy and the ages of the children. We did this one time with our two teenagers to the Melia Cayo Guillermo.
You don't seem to be getting a big response here so perhaps a phonecall to a travel agency would be helpful.
Another suggestion is renting a villa but you would have to do your own cooking or go out for meals. There are a lot of this type of accommodation in the Akumal area of the Mayan Riviera.