I generally combine offsite and an onsite stay with my WDW vacations.
Although I enjoy my stays in WDW accomodations, I've always been bemused by the 'must-stay-at-WDW-cuz it's more magical' view. I've had magical stays during all my Orlando vacations-- including Universal/IOA.
That said, I do like the WDW deluxe hotels and the home-away-from-home accomodations. But, IMO, I feel you get more 'bang for the buck' with offsite accomodations, particularly if you want suite-style accomodations or are considering an offsite hotel on the level of WDW Value or Moderate accomodations.
Some things to consider:
Transportation: Will you have a car (your own or a rental)? Even when staying onsite, I always have a rental car--my idea of vacation is not to be tied to bus schedules--so access to transportation is not a major issue for me. For many people, not having to drive is a big plus to staying onsite. WDW transportation is extensive and runs more frequently than offsite transportation. Although, I've not used the DTD transportation, I understand the busses run pretty frequently.
Dining--Offsite provides accessability to wider variety of restaurants in various price ranges.
You stated a six-night stay. If the Fairy Tale Package is available during your stay, you may want to consider that. For a package, it is very good deal. Basically, you pay for four nights and get three nights free (the package is inclusive of the Ultimate Park Hopper Passes, which provide access to all WDW parks, water parks, Disney Quest, and Pleasure Island). Given the age of your children, those features--eg., Disney Quest, Please Island--may not be as important to you.
So in closing, is it necessary to stay on property to have an enjoyable, magical WDW experience? I don't think so. Whatever you decide, have a terrific vacation!